I put . . . . . . . . my hat when I come home. A. to B. with C. up D. off

The correct answer is D. off.

When you come home, you take off your hat. This is because you are no longer in a situation where you need to wear a hat, such as when you are outside or when you are at work. Taking off your hat allows you to relax and be comfortable in your own home.

The other options are incorrect because they do not make sense in the context of the question. Option A, to, does not make sense because you do not put your hat to anything when you come home. Option B, with, does not make sense because you do not usually carry your hat with you when you come home. Option C, up, does not make sense because you do not usually put your hat up when you come home.