I'm not sure if there are answers to choose from, but it is easy to determine the meaning of "nailed" using context clues.
Based on the fact that Ari saw approval on everyone's faces, the word "nailed" should be a positive word. Any negative words can be eliminated.
In this context, "nailed" means succeeded, aced, did well, got it right, etc. If choosing from several possible answers, choose the one that most closely fits: ...he saw the approval on everyone's faces, he knew he had got it right.