What type of sentence might include a coordinating conjunction

A simple sentence

A compound sentence

A complex sentence

A compound complex sentence

Well, there isn't only one choice here - I'd say a coordinating conjunction is used in a complex and compound-complex sentence.

A coordinating conjunction gives equal emphasis to two (or more) main clauses - a simple sentence is only one main clause, as well as a compound sentence, which is why I wouldn't say those two answers are correct, but the remaining two should be.

A compound complex sentence