How to update my iMac version?

Last night I updated my iPhone to iOS 6.0 and now I can't put music on it because it says iTunes is out of date but I can't install the new iTunes without updating my mac to version "10.6.8 or greater."

So how do I do that?

You have to purchase and install 10.6. The problem is that 10.8 is the latest version. 10.6 was released back in 2009 and is no longer sold because it's too old. You can buy used copies for $80-$350 or so, but it only cost $30 when it was released. Contact Apple's customer support to see if they can recommend a safe place to purchase it. Once you have it, install it and run Software Update until you get to 10.6.8.