How do I save the reg key in premier pro cs6 when uninstalling so I can use it again on another machine?
Is that Key not on the case for the physical media, or in an e-mail from Adobe?
If you bought from Adobe, or Registered (not the same as Activation), you should be able to call that up with your account on Adobe.com.
As Hunt said, your get your key either on a sticker (physical media) or an email from Adobe (online purchase)
The registration key is encrypted inside the program as soon as you enter the key and activate, so someone who "happens by" your computer can't see your key