It's the early 2008 MBP 15" AFAIK, if this is the case it can run 10.8, and if you do so put some extra RAM in it, 6 GB is the Maximum, one 2 GB + one 4 GB.
If you invest a bit more you could also get a SSD in the Optical bay, actually the HD there and the SSD in the main slot, this will greatly improve speed.
You can upgrade your machine to OS X 10.8 Mountain Lion via purchasing Mac OS X 10.6 Snow Leopard for 19 USD from the Apple Online Store and then updating Mac OS X 10.6 Snow Leopard via Software Update to 10.6.8 and then opening the Mac App Store (MAS) in your Applications folder and buying OS X 10.8 Mountain Lion for another 19 USD.
Also know, that your machine can take up to 6 GB of RAM via one 4 GB and one 2 GB 200-pin DDR2 SO-DIMM RAM module, you currently have two 1 GB modules inside it. Mac OS X 10.6 Snow Leopard might run fine with 2 GB, but OS X 10.8 Mountain Lion is better with 4 GB and more.