The correct option is
B The child felt hungry and she began to cry.
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.
Options A: The word, "because" is a subordinating conjunction which connects dependent and independent clauses. The clause, "The child began to cry" is an independent clause. The clause, "because it felt hungry" 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 B: This is a simple sentence as it has only one clause with a single subject and predicate. The subject is "the child" and predicate is "began to cry". The words, "Feeling hungry" is a phrase and not a clause. Hence, this is a simple sentence and this option is incorrect.
Option C: The two clauses viz (i) "The child felt hungry" and (ii) "she began to cry", 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 D is incorrect as option C is the correct answer.