NTW4701BQ0 Amana Washer - Overview

First pry off the cap of the agitator. Then using a socket remove the bolt that holds the plastic cup in place. Remove this cup by prying it loose from the two tabs that hold it in place. Once this cup is removed you can get to the broken cogs.
Slip the new cogs into the underside of the cup, and slide the cup back down in the agitator housing using the slots on the side for a guide. (You may want to remove the entire agitator and assemble everything upside down, then flip it all back over to mount, so the cogs don't fall out).
Tighten the bolt, snap the cap back in place on top of the agitator and your'e done. Easy repair.

The instructions came with the repair kit, it was fairly simple and straight foward.

One bolt held the entire agitator unit in the washer, as well as held the upper and lower halves together. Once that nut was removed the two halves seperated and the plastic clutch pieces could easily be replaced wtih the new onces in the repair kit.

Very easy do-it-yourself repair! Took about 20 minutes because I was being cautious. Next time I could do it in 5 minutes.

On top of the agitator is a flat cap that is held in place by the friction of an o-ring, there are no fasteners. I would imagine one could get under the lip with a small screwdriver or butter knife to pop it off but I chose simply using my fingernails so as to not disfigure the cap. Under the cap you will find the head of the only bolt that holds the assembly together it is a 7/16 head and because it is in a 4" deep well your will need a 6" extension for your ratchet. Once the bolt is out the top of the agitator, the assembly with the cogs removes by hand. Set the assembly upside down on the counter, slide the black plastic ring off, pull the cogs out with your fingertips, install the new cogs put a new black ring on and set the assembly back in the agitator. Reinstall bolt. As the bolt is down in a tube, you cannot set it in place with your fingers and it will fall out of the socket. To hold the bolt in the socket during positioning you can either put a gob of Vaseline on the bolt head to hold it in the socket or form a small piece of paper over the bolt head and set it into the socket, the friction of the paper will hold the bolt into the socket. Took me less then 10 minutes, good luck