HT1366: MacBook: How to find the serial numberLearn about MacBook: How to find the serial number
Yes that's the Late 2008 model 5,1 Aluminum Unibody. That's the first MacBook that can run Mountain Lion.
But to buy and download it you have to access to the App Store which means you have to be running 10.6.8 Snow Leopard.
Mountain Lion will only cost $19.99 but trying to find a DVD for an obsolete OS like Snow Leopard might get pricey
Mountain Lion will require at least 2gb of RAM but really needs 4gb to run smoothly.