Which of the following is a compound-complex sentence?

Fred busied himself with his task, raking the leaves into several piles.

While speaking to George, Fred busied himself among the piles of leaves.

Fred got up, and while he was raking the leaves, he told George a funny story.

Fred liked George, and he raked leaves while telling George a funny story.

Compound-complex sentence is the one that consists of two independent (can function on its own) and at least one dependent (can not function on its own).

Whatever clause may be it must consist of a verb that functions as a predicate. So the easiest way to count the clauses is to count the predicates.

First sentence has only one predicate (busied); raking is a participle, thus can not be counted as a predicate.

Second sentence has only one predicate (busied); speaking is a participle.

Third has three predicates (got up, was raking, told). That means this sentence consists of three clauses.

Fred got up - independent

while he was raking the leaves - dependent

he told George a funny story - independent

Fourth sentence consists of two predicates (liked, raked); telling is a participle.

Only the third sentence meets condition for compound-complex sentence.