Follow these steps to increase your /home partition.
Create a Ubuntu Live USB and boot from it.
Go to Gparted and turn off your swap partition. (Rightclick-->swap off)

Rightclick on swap partition-- > "Resize/Move"--> Move it to the Rightmost area.
Right click on home partition (/dev/sda6) --> "Resize/Move" --> Increase its size by dragging it.
Apply changes.
Now you need to Correct the UUID entries in the fstab file.
(If you move your /boot partition)
Chroot to your original / partition and reinstall grub:
Execute the following commands in sequence.
sudo mount /dev/sda5 /mnt
sudo mount /dev/sda8 /mnt/boot
for i in /dev /dev/pts /proc /sys /run; do sudo mount -B $i /mnt$i; done
sudo chroot /mnt
grub-install /dev/sda
update-grub
exit
Update the UUID entries in fstab file as given below:
Open another terminal and execute :
sudo blkid
Open one more terminal and execute :
sudo gedit /mnt/etc/fstab
Replace the UUID entries of sda6 & sda7 (& sda8 if you move the boot partition too) with those of the output given from the blkid command.
Reboot.
sudo blkidcommand is the one that gives you the UUIDs for the partitions. – Arronical Jun 15 '16 at 09:01sudo blkid. You need to do this on a LIVE usb because you are editing Swap and /boot partition. Otherwise its like Cutting off the branch one is sitting on ! . – Severus Tux Jun 15 '16 at 09:05/etc/fstabhere as moving a partition does not change its UUID. You must only do that if you delete a partition to recreate it elsewhere or if you create an entirely new partition that needs to get mounted automatically at boot. Also, if you don't modify the/boot(or maybe also root/) partition, there's absolutely no need to reinstall GRUB. Even if you moved one of those, I am not sure it would be necessary in any case as long as the order and the UUIDs stay the same. – Byte Commander Jun 15 '16 at 09:45