The correct answer is C. reveal.
To conceal something means to hide it or keep it secret. To state something means to say it in a clear and direct way. To declare something means to say it officially or publicly. To announce something means to tell people about it, usually in a formal way.
In this case, the man is trying to hide the fact that he and his wife are already married. He is doing this by not telling anyone about it, and by trying to avoid situations where people might find out. He is not saying anything about it, and he is not making any public announcements. He is simply trying to keep it a secret.
The other options are not correct because they do not accurately describe what the man is doing. To state something means to say it in a clear and direct way, but the man is not saying anything about his marriage. To declare something means to say it officially or publicly, but the man is not making any public announcements. To announce something means to tell people about it, usually in a formal way, but the man is not telling anyone about his marriage.