HT1338: OS X: Updating OS X and Mac App Store appsLearn about OS X: Updating OS X and Mac App Store apps
I need to run Java 6 on my Mac for software for Phoenix University.
Sorry to say you are probably not going to be able to do that. Apple has chosen not to update Java 6 for Lion / Mountain Lion to a safe version and has disabled it's use in browsers for anybody that already had it.
The best solution I've seen is to install Windows in a Virtual Environment and install Java SE 6 there.