Product review (2 stars): does not fit Whirlpool "thintwin"
This repair kit does not seem to fit the Whirlpool "thintwin" washer Model# LTE6234DQ0, Type# 144-00.  In the end I did make use of the cam dogs.

I have ordered this repair kit for the top part of the agitator called "auger".  This auger helps the clothes to rotate inside the washer from top to bottom fashion by turning in only one direction, each time the whole agitator is in motion.  After some searching on the Web and visual check the four cam dogs that turn the auger in one direction were worn.

I decided to order this kit since it was inexpensive and came with other parts, including the cam dogs that I needed.  After opening the kit and taking apart the auger in the washer to compare them I noticed a big difference.  The most important part, called the agitator cam, that helps hold the cam dogs in place had a much larger dimension for this model washer.  However, I did use the four cam dogs which seemed to be the same size and shape, and thus fixed the problem with the auger not turning.

I tried to make use of some of the other parts such as the o-ring for the cap and seal assembly, but the o-ring was too big to make a good seal.  I re-used the old o-ring.