Complex
A complex sentence contains a dependent clause and an independent clause. A dependent clause cannot stand alone. The dependent clause in this sentence is "Because I already said yes to someone else". This is not a complete thought by itself. The reader is left hanging. The independent clause in this sentence is "I can't go to the dance with you." This is a complete thought that can stand alone. These two elements make up a complex sentence.
A compound sentence is a sentence that has two independent clauses that are joined with a conjunction. As in "I am excited for the dance, so I bought my dress already". Both halves of this sentence are complete thoughts. A compound complex sentence contains a compound sentence and a dependent clause attached to it.