How could have Poirot solved the murder better?

I think poirot could have shared his ideas more with others like Sheppard. Unlike other detective fiction, where the reader (and the narrator) is privy to the detective’s process, Poirot is famously tight-lipped about his investigations. Dr. Sheppard here is commenting on Poirot’s unique access to the case. Sheppard is aware of Poirot making connections and forming hypotheses, but he has no idea how Poirot arrives at those hypotheses, nor even the details of those hypotheses. It is not until the end of the novel when Poirot is certain of his convictions that he will share them with Sheppard (and the reader). Until then, Dr. Sheppard remains confined to guessing Poirot’s ideas. The detective’s ideas are so brilliant that none of the other characters could possibly understand what he’s thinking unless he decides to explain himself.