Write in passive voice
They are painting my office today​

Today my office is painted by them.

The sentence is an example of an example of an unfortunately worded phrase.

A sentence is usually made up of a subject and an object

The subject is the person or item that the sentence is about. The object is the person or item that the action is being done to - the receiver of the action. According to convention, subject usually precedes the object.

In this question, the subject is "my" and the object is the "hat".

Thus, the correct order of the sentence is "throw my hats down the stairs"

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