hangover, hang over

Hangover or hangover ( one word ) means the discomfort or illness felt after drinking too much alcohol --
He has a hangover; there was a party last night.
You know you'll have a hangover if you drink too much.

Hangover may also mean something left behind from a previous state of affairs --
That sign is a hangover from when the building was a tavern.

Hang over or hang over ( two words ) means to be suspended; to dangle ( hang ) above ( over ) --
We should buy a picture to hang over the fireplace.
A cloud seems to hang over his head.

Hang over may also mean to fasten to a wall or ceiling ( hang ) more than ( over ) --
We had to hang over a dozen pictures.
We could hang over twenty posters on that long wall.

Now that you know that, you can say--
"This picture of him with a hangover is just the thing to hang over his desk."

Note --"hungover" ( one word ) is used to describe the feeling of illness or discomfort after drinking to excess --
He's hungover; don't even try to talk to him.

Note # 2 --"hung over" ( two words ) is the past tense ( yesterday, or some time ago ) of "hang", meaning to be suspended or to dangle ( hang ) above ( over ) , literally or figuratively --
The chandelier hung over the table, but then we moved the furniture.
A sense of expectation hung over the crowd.

Hung over may also be the past tense of "hang", meaning to fasten to a wall or ceiling, or to suspend from a height of some kind ( hang ) more than ( over ) --
He hung over a hundred pictures today.

Not to be confused with "overhang", meaning to be suspended over, literally or figuratively --
The chandelier should overhang the table.
Gloom will overhang the guests when they hear the bad news.

Overhang also means the upper part of a building that sticks out beyond the lower wall --
This building has an overhang of about three feet; the upstairs room is larger than the downstairs.