read the dictionary entry.

hamper
v. to make it difficult for someone to do something
n. a large box or basket

which sentence uses hamper as a verb?
they hamper the investigation when they ask too many questions.
put the dirty clothes in the hamper in the bathroom.
we brought a hamper of food to the picnic last weekend.
they keep all the toys in a special hamper next to the door.

The sentence that uses hamper as a verb is - They hamper the investigation when they ask too many questions.

Explanation:

As explained above, the meaning of the verb 'hamper' is to prevent someone from doing something easily. The synonyms of this verb would be - to hold back, to hinder, to impede, to obstruct, etc.

In this case, it is implied that, the more questions people ask, the harder it becomes to carry out the investigation. This is the only sentence where this word is used as a verb, while in the rest of the sentences 'hamper' is used as a noun.

can you provide the possible answers

3 is blunder, i’m not sure about the last one but the first two look correct