His way of doing things was different than what the previous instru

The first thing we should notice is that the correct idiom is different from. Accordingly choices A, B, and E can immediately be eliminated.

We want to compare "His way" (whoever he is) to the way of the previous instructor. Presumably D accomplishes this (the word that taking the place of the way). Yet the "official answer" is (C). I cannot explain it. Normally we use "the previous instructor did" when we are comparing two actions. For example you might say:

Carlos liked football more than Maria did.

Because if you just say:

Carlos liked football more than Maria.

Then we're not sure whether Carlos liked football more than Maria liked football or whether Carlos liked football more than Carlos liked Maria.

If you have written this question, at the very least I recommend adding a name at the beginning something like:

John's way of doing things...