Can I upgrade iPhone 4 iOS 4.3.3 to iOS 6.1.2 and not higher so I can jailbreak it?

My iPhone 4 is jailbroken on iOS 4.3.3 and I want to upgrade to iOS 6.
I read that I can download the iOS from a sit to upgrade, will it work?

There's no jailbreka out for iOS 7 But available jailbreak for iOS 6.1.3, so if you upgraded your devices you can able to jailbreak your phone easily

Since your iPhone is currently jailbroken, check the SHSH's you have available on cydia.
The shown versions are the only one you can update or restore you iPhone to