The correct option is
B Some people believe in astrology and consult astrologers frequently.
A simple sentence has only one subject and predicate. It has a finite verb with a completed thought. A compound sentence has at least two parts (also referred to as a clause). Each part has its own subject and predicate and makes good sense by itself. Hence each clause is independent of the other and called the main clause or independent clause. The main clauses are connected using a co-ordinating conjunction (for, and, nor, but, or, yet, so).A complex sentence has at least one main clause (which is an independent clause) and one or more dependent clauses, connected using a subordinate conjunction. The dependent clause cannot stand by itself and make good sense. It depends on the main clause.
Option A: The two clauses viz (i) "Some people believe in astrology" and (ii) "They (implied) consult astrologers frequently", can stand independently and make good sense. They are independent clausesconnected using the co-ordinating conjunction-"and". Hence, this is a compound sentence and this answer is correct.
Option B: "As" is a subordinating conjunction which connects dependent and independent clauses. The clause, "Some people consult astrologers frequently" is an independent clause. The clause, "as they believe in astrology" cannot stand by itself and make good sense. It is a dependent clause. Hence, this is a complex sentence and this option is incorrect.
Option C: This sentence has only one clause with a single subject ("Believing in astrology") and predicate ("makes people consult astrologers frequently"). Hence, this is a simple sentence and this option is incorrect.
Option D is incorrect as option A is the correct answer.