I own a Ford F-350 Power stroke 7.3, for a little bit more than 3 years now.
I installed a 6" lift kit and finally took it off road. For some reason when I hit the 4H or 4L it make a sound on the differential like something is braking.
At one point it gear back by itself to 2H from 4L.
I don’t know much about transmissions .
The 2H works no problem. My question is should I concentrate on the Transmission or the differential?
thank you  

Sounds like you should be looking at transfer case.  

What is a transfer case snoman?

Thank you,
power truck  

Transfer case is bolted behind tranny and enables you to send power to both axles on demand and also has low range too.  

So you think I should have that checked before evrything else. I just want to make sure I dont get screwed by mechanic shops.

Thank you,  

Your symptoms DO NOT point to a tranny problem. And the fact they it shifts ranges on its own says something is not right with transfer case.  

Drain the oil in transfer case and check for excessive metal in oil. Also check driveline yokes for clearance. See if they are binding. grab driveline and roll by hand, see if something is binding. make sure your gearing is correct. If 4.10 in rear needs to be 4.10front or 4.09 for front. I sometimes set truck up on jackstands and roll drivetrain by hand in weird situation like you having. Just watch everything go round, amazing what you can learn just laying their. On driveline yoke spray with black paint and roll around and see if paint is getting rubbed off. If so yoke bind is a problem. good luck.