86 Blazer 4 wheel drive

[hshoer1]

Nice board gentlemen. :-)
My son has a 86 blazer 4 wheel drive, he said if he hits the brakes it pops out of gear, from low to high or high to low.
I know nothing about 4x4's so trying to get an idea of what he has going on, guessing transfer case?
He is in College in Florida and I'm in California, can't even look at it.
He said he took it to a shop and they wanted $450.00 just to look at it and give him an idea of what is wrong.
Thank you for you time gentlemen,
Brian