Verified Answer :

In
the sentence:

Mother
reads him three stories before bedtime.

The
pronoun which is ‘him’ is used as a direct object.

A pronoun is used to
substitute a noun. In order for it to substitute, it must have a clear
antecedent.

Their answer is wrong, actually.

First, we know that it cannot be A (object of preposition) because their is no preposition.

Second, it cannot be C (direct object) because a direct object recieves the verb. In this case, stories recieves the verb reads.

So, it must be an indirect object (B) because an indirect object answers the questions to whom?

So the answer is (B) indirect object because him answers the question to whom?