hard disk is not showing full space

Select the hard drive icon on the desktop or in the Finder window and perform Get Information. (Command I or under the File Menu.) In the top of the Drive dialog you'll see something like Capacity: 128 GB and below it Available: 60GB and below that Used: 68 GB. I suspect/hope that the 60GB you mention is either available or used.

If it is actually showing Capacity: 60GB then there is a potential problem. To dig further if this is the case, find Disk Utility in the Utilities folder of your Applications folder and start it. If you have any external drives or flash drives connected to the computer, remove them for the moment. In the left window pane of DU you should see one disk icon under the word Internal. If you see two that means the hard drive has been partitioned (split in two) and that is why your startup drive shows less capacity than you expected. If you see only one icon click on it and run First Aid. Report back what you see.