my mac mini build is 11G56 and mac osx is 10.7.5 how can i install latest mac 10.8 and above

Simply purchase Mountain Lion from the App Store and it will begin installation after the download is complete. Note that it's a large download, about 4.5GB, so you should have a good Internet connection..

However... if I were you, I would just wait another month or so until Apple releases Mavericks - the 'latest' announced version of OS X -> http://www.apple.com/osx/preview/.

No need to pay for two upgrades in a months (or so) time...

Clinton