I have a 1997 Ford Explorer XLT 4.0 V6. My transfer case went out on it a few weeks ago and I need to know which kind of transfer cases are compatible for my vehicle. The Tag states: 4405-08 and part # F77A-GA. Also how hard would it be to replace by myself with some mechanic skills. I have been reading around and need to find the right answer. If someone could help, it would help a lot! Thanks!

 

That looks like one of the Torque-On-Demand cases, not sure how compatible they are though.
As far as changing it, it's a royal pain. I'm doing a transmission right now, and it's not fun. It looks like it came from your area underneath, so all the bolts are corroded and torque to about 400tf/lbs. It's easier to get to the bolts than a Jeep case, but there's one that you may well need to pull the exhaust to get to. That's just what I ran into on my 95.