* "Hide" is a verb. It means to conceal oneself.
* "Out" is a preposition. It can indicate location, direction, or state.
The problem with "hide out" is that it combines a verb and a preposition in a way that doesn't make sense grammatically. You wouldn't say "walk out" or "eat out" in the same way.
So, what's the right way to say it?
There are a few options:
* "Hide" alone is perfectly fine: "The thief hid in the woods."
* "Hide away" is more common than "hide out" and is grammatically correct. "The thief hid away in the woods."
* "Go into hiding" is a more formal phrase. "The witness went into hiding after the trial."
While "hide out" is widely used and understood, it's not technically grammatically correct.