"아이가 괴물을 무서워해요."
Translation:The child is afraid of the monster.
its a bit weird to explain but 어/아하다 makes the adjective into a verb that uses 를/을, so
괴물이 무섭다 the monster is scary
아이가 괴물을 무서워한다 the child finds the monster scary
the most common and clear example of this i can think of are the verbs 좋아하다 and 싫어하다 from adjectives 좋다 and 싫다
you will also see it in cases where people are acting in "adjective" way
부끄럽다 to be shy, embarrassed
부끄럽지 않아요 im not embarrassed
부끄러워하지 마세요 dont be/act embarrassed
From what I was able to find 두렵다 expresses supposition. As in, you have fear of something that hasn't happened, or you think might happen.