help with operating system

You can update it to OS X 10.8 Mountain Lion.

 

It should run Mountain Lion. But, with only 2GB of RAM it wouldn't run well. It might run OK with the max 6GB RAM, depending on the programs you use.

 

I believe my iMac is the exact same machine as yours (I'm away from home currently so I can't check directly). Mine is an "Early 2008" 24" Aluminum Core 2 Duo and if I remember correctly it's 2.8 GHz.

However, I've got 6 GB RAM in mine (even though Apples specs give a max of 4 GB, it works with a 2 GB stick and a 4GB stick). You might want to consider doing the same.

I'm currently running OS X 10.6.8, but my understanding is that this machine will run Lion and Mountain Lion. 10.8.4 is the latest version.

Within a week or two I'll be doing a big (and maybe crazy) upgrade to my iMac. I'll be removing the optical disc drive and installing an SSD and larger HDD, and upgrading the OS to 10.8.4. I plan on using Terminal commands to combine the two storage drives into one home-made Apple "Fusion" drive.

Any one of those things might be problematic, but I think the OS upgrade is least likely to cause problems.

Oh, I almost forgot: I have installed 10.8.3 on a spare Firewire drive, and it boots and appears to run fine on this old machine. I even did some entry-level iOS programming with Xcode without trouble.

Let me know if you've got any questions about our iMacs.