A compund-complex sentence combines both a compound sentence and a complex sentence, meaning it contains an independent clause and a dependant clause.
<em>"My cat is so finicky that he never eats the food I get him" </em>is the independent clause, as both the subject (my cat) and predicate are present and explicitly defined.
<em>"he meows and meows for something different." </em>is the dependent clause, given that the subject is undefined - it is known that the subject is "my cat" due to the clause's dependency with the first clause.