“That makes me think he has something to hide.”

Your sister is telling you about her husband, who's been coming home late recently. Your sister confronted him about it, and he got angry about it. You think that he probably got angry because he's doing something wrong. You say:

That makes me think he has something to hide.

that makes me think (clause)

This phrase is used when you're trying to make guesses about something, or when you're trying to figure out what something means. When you find evidence or a fact that brings you to a certain conclusion, you say "that makes me think ___":

Hmm... his office light is still on. That makes me think he might still be around here somewhere.

(someone) has something to hide

When a person "has something to hide", it means that they have done something wrong that they don't want people to know about. "Having a secret" has a neutral meaning, but "having something to hide" carries a negative connotation. Some other examples include:

Why don't you want to show it to me? Do you have something to hide?

Go ahead. I've got nothing to hide.