Here is an explanation...

This question is primarily testing IDIOMS and MEANING.

When we have a verb like CONVINCE, what follows depends on what part of speech we're looking at. Consider the following:

I am convinced of your innocence.

I am convinced that you are innocent.

Both of these sentences are correct. In the first, the thing that I'm convinced of is a noun - "your innocence." When the object of the verb CONVINCE is a noun, we use OF. In the second sentence, the thing I'm convinced of is a clause - "you are innocent." When the object is a clause, we use THAT.

In this sentence, the object should be a clause - "social work belongs in the university" - so we need THAT. Eliminate A, C, and E.

In B, AND WHERE turns what comes after into a separate clause idea - this changes the meaning, and doesn't quite make sense. We want those ideas connected with WHERE, so the answer is D.