If iTunes says you have the latest version of iOS for your device then you can't upgrade further. A bit unfair but that's just the way things are. Later iOS versions need better hardware to run. The iPod Touch 4 can run iOS 6 (although it won't have Siri) and as far as earlier versions of the iPod Touch are concerned, I'm not too sure but the Wikipedia entry on iPod Touches would have the answer.
Requirements: Compatible with iPhone, iPod touch, and iPad. Requires iOS 4.0 or later
Than means you need a 2G or later iPod. Since you say you have 2x I suspect you have a 1G iPod since those can only go to 2.x via iTunes. The 1G can go as high as 3.1.3 that you get here