A noun clause is a dependent clause that acts as a noun, working as the subject, the object of a verb or preposition, or the complement. Noun clauses often begin with words like that, if, whether, what, who, when, where, why, and how.
The distinction this exercise tests:that and what can look interchangeable, but they play very different roles.
Use that when the clause is already complete: it has its own subject and verb, and nothing is missing: I know that he is honest. (he is honest = complete on its own) She said that she was tired.
Use what when something is missing from the clause:what itself fills that gap, meaning “the thing(s) that…”: I'm interested in what he thinks. (he thinks ___; what fills the gap) What you decide doesn't matter. (you decide ___; what is the missing object)
Quick test: try removing the word. If the rest of the clause still makes a complete sentence on its own, use that. If it doesn't (something's clearly missing), use what.