To install OS X Mountain Lion in four computers, just download it in one Mac. Then, open Finder, go to Applications folder and copy the Mountain Lion installer to an external disk. You will be able to use that copy to upgrade all your computers.
Another thing you can do is to create a bootable drive instead of copying the OS X Mountain Lion installer. This will simplify the upgrading process of a Mac with Mac OS X Tiger or Leopard. To do it, after finishing the OS X Mountain Lion download, use an application like Lion Diskmaker to create a bootable USB drive or DVD > http://liondiskmaker.com
If you have 10.5.6 as your information line indicates, you must first upgrade that computer to Snow Leopard, 10.6, by buying the install disk for $20 from the Apple on-line store.
You also need to check that each computer you want to install on is compatible, see http://www.apple.com/osx/specs
Then, download the ML installer, $20 from the Mac App Store, and do not let it install. Instead, make a copy of the installer file found in Applications to a safe place, like your documents folder...the installer destroys itself as its last step.
With a safe copy, install on the first machine. If the machines are networked, just copy the installer to each machine and then run it. If they are not networked, then you can build an installer flash drive, has to be an 8 GB flash drive since the installation is 4.5 GB.