This downgrading tutorial only applies to iPhone 4s and iPad 2 (Product type: iPad2.1, iPad 2.2, iPad 2.3 and iPad 2.4). You can check the product type of your device on 3uTools, then download the corresponding firmware.
I am currently trying to jailbreak my iPod touch 4g on 6.1.6 with a Windows 7 VM (as I am on Arch Linux (but I do have a Windows PC, but THAT never worked either.)), so I'll tell you how that goes.