I think you are referring to a 4th generation iPod Touch? As the 4th gen white iPod in the picture doesn't require a password.
Simplest method is to hook it to iTunes and restore it. It will delete everything (but since you bought it, you probably don't want somebody else's stuff anyways).
I feel like you may have bought it from somebody who stole it, if they can't remember the password. You can look up the IMEI or serial number on Apple's website to see if it's been reported stolen. But like I said, just hook it to iTunes and restore it.