"Put on your jacket, take it off, hang it up, take it down, and pick it up" - Mr. Han

take something   off

to remove something, especially a piece of clothing from your/ somebody's body

He sat on the bed to take his boots off.

Charlie was taking off his shirt when the phone rang.

OPPOSITE put on

He took off his uniform and put on a sweater and trousers.

I'll have to put my glasses on; I can't read the sign from here.

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take down = to lower your underwear or trousers without taking them off

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Riddle

I take off my clothes when you put yours on and I put my clothes on when you take yours off what am I?