Can I update from iOS 5 to iOS 6 on iPhone 4? I don't want to update to iOS 7 on this iPhone 4 and since I'm borrowing it from a friend, I don't want to jailbreak it either. 

It's not a matter of downgrading to iOS 6, it's still an upgrade since I'm currently running iOS 5.1, I just need to know where to find the update and how to go about doing it.
There is no Apple supported way to update an iOS devices OS except to the latest current OS release that runs on that device (or a beta OS, if it is strictly a test device and you are a registered developer).  Apple no longer signs (which includes vouching for the security of) any earlier OS releases (except for old devices, such as an iPhone 3GS).