The sentence '你最好别告诉他答案’ means 'You'd better not tell him the answer.'
你(You) 最好别(had better not) 告诉他答案(tell him the answer)。
别告诉他你最好(的)答案. In this sentence, you need insert a '的'. But if you say like this, it is a little weird. We often '别告诉他你的答案', as the answer often is unique.