How do you adjust the carberator on the B & S Intek 16.5 Engine?

Besides the idle control on the butterfly there is no adjustment
Some have a air mixture for low speed .it has a black cap on it.
Its on the side of the carb.

Maybe if you tell us what issue you have with the engine we can help because you are not going to adjust this carb.

I have B&S 1220070139B8 that will start and run on full choke. When I take it off full choke to no choke, it dies. I was successful to get it to stay running on the 3rd notch (3/4 choke).

Any ideas?

Remove and clean the bowl and needle valve with a carb cleaner. Reinstall and see if it runs any better. Also try adding an ounce of SeaFoam carb cleaner to a tank of fresh gas and allow to run for an hour on partial choke. Sounds like your carb is dirty and not giving enough fuel to the mix