How can i extend my partition further than the limit? Disk Utility
Your Mac officially doesn't support Mountain Lion so the how-to below may fail!



You can't move ("backward-expand") the beginning of an existing partition to "lower" physical block numbers (with 0: the first block and 234441647: the last block and your Mountain Lion partition starts somewhere in the middle) with Disk Utility.

You will be able to create a new partition in the unallocated disk space and restore your existing Mountain Lion partition to it though. Then remove the old partition and expand the new one to the full size.

Since your Mac can't boot to Internet Recovery Mode, you need a second boot media (e.g. a thumb drive) with a basic system or a full fledged system.


Create a bootable Lion thumb drive
Boot to the thumb drive
Open Terminal and enter diskutil list and (assuming your internal disk has the disk identifier disk0) sudo gpt -r show disk0 to get an overview
Unmount your internal disk:

diskutil umountDisk disk0

Add a partition in the unallocated disk space:

sudo gpt add -i 4 -b 409640 -s 117650752 -t 48465300-0000-11AA-AA11-00306543ECAC disk0

Enter diskutil list and get the identifier of the new partition with the size 60.2 GB (your original ML volume has the size 57.1 GB). This may be disk0s2 or disk0s4
Format the partition with newfs_hfs:

newfs_hfs -v "New" -J /dev/disk0sX #use the proper identifier here

Close Terminal and open Disk Utility
Restore the Mountain Lion volume to New.
Boot to the restored Mountain Lion volume (AFAIR you will see two volumes with the name Mountain Lion in StartVolume, so boot to the proper one!) to check if it works.
If everything works open Disks Utility and remove the second Mountain Lion partition. Expand the first Mountain Lion to the full size.