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as per @steeldriver comment i tried the journalctl with extra arguments here is the results. but unfortunaltely I can't able to run fsck manually on /dev/sda3 manually. because it shows the target is busy. it's my root partition.

as per @steeldriver comment i tried the journalctl with extra arguments here is the results. but unfortunaltely I can't able to run fsck manually on /dev/sda3 manually. because it shows the target is busy. it's my root partition. And I got this message during unmounting the /dev/sda3

EDIT:

as per @steeldriver comment i tried the journalctl with extra arguments here is the results. but unfortunaltely I can't able to run fsck manually on /dev/sda3 manually. because it shows the target is busy. it's my root partition.

Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: Internal clock never stabilised.
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============ SDHCI REGISTER DUMP ===========
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Sys addr:  0x00000000 | Version:  0x0000c001
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Blk size:  0x00000000 | Blk cnt:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Argument:  0x00000000 | Trn mode: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Present:   0x01f70000 | Host ctl: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Power:     0x0000000f | Blk gap:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Wake-up:   0x00000000 | Clock:    0x00001003
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Timeout:   0x00000000 | Int stat: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Int enab:  0x00ff0083 | Sig enab: 0x00ff0083
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ACmd stat: 0x00000000 | Slot int: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Caps:      0x21e608b2 | Caps_1:   0x00002077
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Cmd:       0x00000000 | Max curr: 0x00000064
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[0]:   0x00000000 | Resp[1]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[2]:   0x00000000 | Resp[3]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Host ctl2: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============================================
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: Internal clock never stabilised.
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============ SDHCI REGISTER DUMP ===========
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Sys addr:  0x00000000 | Version:  0x0000c001
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Blk size:  0x00000000 | Blk cnt:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Argument:  0x00000000 | Trn mode: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Present:   0x01f70000 | Host ctl: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Power:     0x0000000f | Blk gap:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Wake-up:   0x00000000 | Clock:    0x00001003
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Timeout:   0x00000000 | Int stat: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Int enab:  0x00ff0083 | Sig enab: 0x00ff0083
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ACmd stat: 0x00000000 | Slot int: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Caps:      0x21e608b2 | Caps_1:   0x00002077
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Cmd:       0x00000000 | Max curr: 0x00000064
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[0]:   0x00000000 | Resp[1]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[2]:   0x00000000 | Resp[3]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Host ctl2: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============================================
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: Internal clock never stabilised.
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============ SDHCI REGISTER DUMP ===========
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Sys addr:  0x00000000 | Version:  0x0000c001
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Blk size:  0x00000000 | Blk cnt:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Argument:  0x00000000 | Trn mode: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Present:   0x01f70000 | Host ctl: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Power:     0x0000000f | Blk gap:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Wake-up:   0x00000000 | Clock:    0x00001003
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Timeout:   0x00000000 | Int stat: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Int enab:  0x00ff0083 | Sig enab: 0x00ff0083
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ACmd stat: 0x00000000 | Slot int: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Caps:      0x21e608b2 | Caps_1:   0x00002077
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Cmd:       0x00000000 | Max curr: 0x00000064
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[0]:   0x00000000 | Resp[1]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[2]:   0x00000000 | Resp[3]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Host ctl2: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============================================
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: Internal clock never stabilised.
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============ SDHCI REGISTER DUMP ===========
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Sys addr:  0x00000000 | Version:  0x0000c001
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Blk size:  0x00000000 | Blk cnt:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Argument:  0x00000000 | Trn mode: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Present:   0x01f70000 | Host ctl: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Power:     0x0000000f | Blk gap:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Wake-up:   0x00000000 | Clock:    0x00001003
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Timeout:   0x00000000 | Int stat: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Int enab:  0x00ff0083 | Sig enab: 0x00ff0083
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ACmd stat: 0x00000000 | Slot int: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Caps:      0x21e608b2 | Caps_1:   0x00002077
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Cmd:       0x00000000 | Max curr: 0x00000064
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[0]:   0x00000000 | Resp[1]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[2]:   0x00000000 | Resp[3]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Host ctl2: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============================================
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: Internal clock never stabilised.
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============ SDHCI REGISTER DUMP ===========
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Sys addr:  0x00000000 | Version:  0x0000c001
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Blk size:  0x00000000 | Blk cnt:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Argument:  0x00000000 | Trn mode: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Present:   0x01f70000 | Host ctl: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Power:     0x0000000f | Blk gap:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Wake-up:   0x00000000 | Clock:    0x00002003
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Timeout:   0x00000000 | Int stat: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Int enab:  0x00ff0083 | Sig enab: 0x00ff0083
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ACmd stat: 0x00000000 | Slot int: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Caps:      0x21e608b2 | Caps_1:   0x00002077
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Cmd:       0x00000000 | Max curr: 0x00000064
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[0]:   0x00000000 | Resp[1]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[2]:   0x00000000 | Resp[3]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Host ctl2: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============================================
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: Internal clock never stabilised.
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============ SDHCI REGISTER DUMP ===========
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Sys addr:  0x00000000 | Version:  0x0000c001
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Blk size:  0x00000000 | Blk cnt:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Argument:  0x00000000 | Trn mode: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Present:   0x01f70000 | Host ctl: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Power:     0x0000000f | Blk gap:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Wake-up:   0x00000000 | Clock:    0x00002003
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Timeout:   0x00000000 | Int stat: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Int enab:  0x00ff0083 | Sig enab: 0x00ff0083
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ACmd stat: 0x00000000 | Slot int: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Caps:      0x21e608b2 | Caps_1:   0x00002077
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Cmd:       0x00000000 | Max curr: 0x00000064
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[0]:   0x00000000 | Resp[1]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[2]:   0x00000000 | Resp[3]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Host ctl2: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============================================
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: Internal clock never stabilised.
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============ SDHCI REGISTER DUMP ===========
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Sys addr:  0x00000000 | Version:  0x0000c001
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Blk size:  0x00000000 | Blk cnt:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Argument:  0x00000000 | Trn mode: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Present:   0x01f70000 | Host ctl: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Power:     0x0000000f | Blk gap:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Wake-up:   0x00000000 | Clock:    0x00004003
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Timeout:   0x00000000 | Int stat: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Int enab:  0x00ff0083 | Sig enab: 0x00ff0083
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ACmd stat: 0x00000000 | Slot int: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Caps:      0x21e608b2 | Caps_1:   0x00002077
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Cmd:       0x00000000 | Max curr: 0x00000064
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[0]:   0x00000000 | Resp[1]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[2]:   0x00000000 | Resp[3]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Host ctl2: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============================================
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: Internal clock never stabilised.
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============ SDHCI REGISTER DUMP ===========
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Sys addr:  0x00000000 | Version:  0x0000c001
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Blk size:  0x00000000 | Blk cnt:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Argument:  0x00000000 | Trn mode: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Present:   0x01f70000 | Host ctl: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Power:     0x0000000f | Blk gap:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Wake-up:   0x00000000 | Clock:    0x00004003
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Timeout:   0x00000000 | Int stat: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Int enab:  0x00ff0083 | Sig enab: 0x00ff0083
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ACmd stat: 0x00000000 | Slot int: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Caps:      0x21e608b2 | Caps_1:   0x00002077
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Cmd:       0x00000000 | Max curr: 0x00000064
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[0]:   0x00000000 | Resp[1]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Resp[2]:   0x00000000 | Resp[3]:  0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: Host ctl2: 0x00000000
Jun 28 11:44:39 HaLF-MenTaL kernel: mmc0: sdhci: ============================================
Jun 28 11:44:53 HaLF-MenTaL systemd-fsck[982]: fsck failed with exit status 36.
Jun 28 11:44:53 HaLF-MenTaL systemd[1]: Failed to start systemd-fsck@dev-disk-by\x2duuid-0b05db49\x2dfda2\x2d4e64\x2d96df\x2d0bfda97f0be4.service - File System Check on /dev/disk/by-uuid/0b05db49-fda2-4e64-96df-0bfda97f0be4.
░░ Subject: A start job for unit systemd-fsck@dev-disk-by\x2duuid-0b05db49\x2dfda2\x2d4e64\x2d96df\x2d0bfda97f0be4.service has failed
░░ Defined-By: systemd
░░ Support: http://www.ubuntu.com/support
░░ 
░░ A start job for unit systemd-fsck@dev-disk-by\x2duuid-0b05db49\x2dfda2\x2d4e64\x2d96df\x2d0bfda97f0be4.service has finished with a failure.
░░ 
░░ The job identifier is 40 and the job result is failed.

What I Tried: I followed this answer to exit from the emergency mode. See the logs below while following this method.

What I Tried:

I followed this answer to exit from the emergency mode. See the logs below while following this method.

UPDATE:

After going through the logs, I see that there is an issue with the mount of my HDD (sda) partitions. so I did lsblk and saw that my /home partition which is sda4 is not mounted and after mounting the partition, restarted the Display Manager and I successfully logged in to my Ubuntu through Display Manager. Here is what i did.

a-sajjad72@HaLF-MenTaL:~$ lsblk | grep sda
sda      8:0    0 298.1G  0 disk 
├─sda1   8:1    0     1G  0 part /boot/efi
├─sda2   8:2    0    16G  0 part [SWAP]
├─sda3   8:3    0   100G  0 part /
└─sda4   8:4    0   181G  0 part
a-sajjad72@HaLF-MenTaL:~$ sudo mount /dev/sda4
a-sajjad72@HaLF-MenTaL:~$ lsblk | grep sda
sda      8:0    0 298.1G  0 disk 
├─sda1   8:1    0     1G  0 part /boot/efi
├─sda2   8:2    0    16G  0 part [SWAP]
├─sda3   8:3    0   100G  0 part /
└─sda4   8:4    0   181G  0 part /home
a-sajjad72@HaLF-MenTaL:~$ sudo systemctl restart gdm3

But the emergency mode is still there. and also I have to do this at every boot to made my login. What will be solution.