Iphone 4 stuck in recovery mode loop (non-jailbroken)

This is frustrating me to no end!! I tried to update my iphone 4 to IOS6 via itunes, didn't work because my mac needed at least itunes 6.3.1 but it said everything was up to date. So i tried using a newer mac with an updated itunes, failed after about an hour, & got stuck in the recovery mode loop. Everytime i try to connect to itunes & restore my phone to update, a message pops up saying "could not be restored. this device isn't eligible for the requested build". I've been watching youtube videos for about this for an hour now, nothing. I'm about to go insane, so if anyone has any idea of how i can get out of the loop, that'd be great!!