Final answer:
Hamlet asks the guards to keep his intention to see the ghost of his father a secret so that he can have a genuine and uninterrupted encounter with the ghost.
Step-by-step explanation:
Hamlet asks the guards to keep his intention to join them in seeing the ghost of his father a secret because he wants to have a chance to observe the ghost without any interference or distractions. He wants to ensure that the ghost appears again and wants to be the first person to speak to it, as he believes it may have important information about his father's death. By keeping his plans a secret, Hamlet can have a more genuine encounter with the ghost and have a chance to gather more evidence for his suspicions.