How to adjust 8-3/4" axle bearing preload?

...(next on the right side) adjust the end play to zero then back off the adjuster 4 notches...

I assume you mean the end play is measured on the adjustable right side?
How does the adjuster do its job? Do I turn it clockwise or counter-clockwise to tighten (remove end play)? What does it have to do with the left side axle end play? What's going on inside the differential?

The adjuster has alternating tabs turned down towards the axle shaft. The other tabs I guess are left upwards to provide a surface to tap with a punch/drift to rotate the adjuster. Turning it counter-clockwise backs the adjuster outward towards the axle flange; clockwise moves it inward towards the axle tube.

Am I wanting to back the adjuster out so that the turned-down tabs to make contact with the nearby machined lip on the axle, or does that not have anything to do with removing end play? Or do I want to move it inward (what that does I'm not sure).

The rearend is off the car sitting on some jack stands. What do I do to check the end play, just pull out on the axle flange with my hands, or do I need pry out on it harder with something?

Hang in there with me, I'll get this thing figured out with a little more help.

Jerry