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