The question you ask is too involved for a proper answer. You need to go to a car parts store, and get a repair manual for your car. They cost about $16.00 Or, go to a Public Library.
Newer answer:
A Chilton or Haynes manual will not help you through the process, so don't waste the money or time trying to go that route. Try automotiveforums.com there is a Blazer specific forum where how to's are posted with photos. I believe that the heater core how-to posted there is for a 98 Blazer, but the fundamentals are still the same for a 96. Good luck! Dawn
Another New :
The Chilton manual helped me quite a bit. I changed the heater core on my wife's 96 Blazer. It involves removing the entire dash. It is a very long and involved process and should only be attempted if you are a fairly good mechanic. I have a 98 Blazer and the process is not the same for this vehicle. On the 98, the firewall must be cut to access the heater core. Dennis
with your hands
That's what I am asking you. How do you replace a parking brake handle on an S-10 1996 Chevy Blazer?
you probably have a bad heater core.
its more likely to be the intake gaskets.
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A 1996 Chevy Blazer Does have a transfer case IF it is equipped with 4 wheel drive
Pry up clip on ends and pull off.