Answer: The sentence that is a compound-complex sentence is B. the cat lived in the backyard, but the dog, who knew he was superior, lived inside the house.
Explanation: A compound-complex sentence is a sentence made up of a compound sentence and at least one complex sentence. While a compound sentence includes two independent clauses joined by a coordinating conjunction, a complex sentence includes an independent clause and a dependent clause which is introduced by a subordinating conjunction. B. is a compound-complex sentence because it is made up of a compound sentence, that is to say two independent clauses ("The cat lived in the backyard" and "The dog, who knew he was superior, lived inside the house") and a complex sentence, that is to say an independent clause ("The dog lived inside the house") and a dependent clause ("who knew he was superior").
