We know that women will continue to hold such high positions as cabinet member and governor, but when will a woman win the Presidency?
This sentence is a compound-complex sentence. This is because it has independent clauses and subordinate (dependent) clauses.
A simple sentence has one clause. For example, this is a simple sentence.
Women will continue to hold high positions.
This sentence is a simple sentence because it has one subject (women) and one verb (will continue) and expresses a complete thought.
A subordinate clause, on the other hand, is not a complete thought. For example, this is a subordinate clause.
that women will continue to hold such high positions.
It has a verb, and it has a subject, but it does not express a complete thought because it has “that”, and “that” is connecting it to the independent clause “we know.” Although “we know” is short, it has one subject and one verb.
A complex sentence has at least one independent and subordinate clause, so why is this one compound complex? Because it has two independent clauses. The last clause is an independent clause:
When will a woman win the Presidency?
The clause at the beginning of the sentence, “we know”, is an independent clause. Therefore, the sentence is compound-complex.