It is Snowball who reduces the seven principles of Animalism to "four legs good, two legs bad." He does this after he realizes that many of the animals simply find seven principles too many to grasp. He knows he needs a simpler slogan that the other animals can remember easily and understand. This simpler slogan communicates that animals are good and humans are bad.

At the end of the story, the other animals notice that Squealer has taken the sheep aside to a separate field. Squealer says he is teaching them a new song. He keeps them away from the other animals for a week. Squealer teaches the sheep to chant a new variation on the familiar slogan, changing it to the following: "four legs good, two legs better."

When the pigs then emerge walking on their hind legs like humans, the other animals are dumfounded. It is at this point that the sheep begin their new chant: "four legs good, two legs better."

The answer to this question can be found very close to the beginning of Chapter 3.  The answer is that it is Snowball who comes up with this way of boiling down the commandments.  He says that if any animal could just remember this idea, they would be safe from being bad like the humans.

This sort of goes along with the idea in the beginning of this chapter that most of the animals were just too dumb to learn much.  Because they were too dumb, Snowball needed to make the commandments simpler so that everyone could understand them.