There is not 6G iPod touch. The latest is still the 5G.
What version of iTunes is installed?
iOS devices like the iPod touch use different drivers than plain iPods
What exactly happens when you try to sync?
Does iTunes see the iPod?
Was the iPod previous synced to another iTunes library/computer?
Have you successfully synced from this iTunes library/computer before?
If so have you done anything like update iTunes on the computer since it last successfully synced?
Do the songs play in iTunes?
Does any media now sync to the iPod?
Do you have the right boxes checked to sync?
iTunes: Syncing media content to iOS devices and iPod
Try syncing using the manual method
Managing content manually on iPhone, iPad, and iPod