Answer: NK-1 antagonist.
Start with the job of the drug. Aprepitant is given to stop the delayed (late-onset) vomiting that follows chemotherapy. Vomiting starts when a chemical called substance P binds to the NK-1 (neurokinin-1) receptor in the brain's vomiting centre. So a drug that blocks this receptor will switch the signal off.
An antagonist blocks a receptor; an agonist turns it on. To stop vomiting we must block it, not turn it on, so the answer has to be an antagonist. That removes option 2 (NK-1 agonist), which would instead cause vomiting.
Now choose the right receptor number. Substance P acts on NK-1, so the drug must target NK-1, not NK-2 or NK-3. That removes option 3 (NK-3) and option 4 (NK-2).
Only one choice is both an antagonist and aimed at NK-1. Aprepitant is an NK-1 antagonist (option 1). In real use it is added to a 5-HT3 blocker and a steroid for stronger control of chemotherapy sickness.