The Asian Development Bank was established in 1966 to fund infrastructure and poverty reduction projects across Asia. Its headquarters location is fixed by its founding charter.
Since only Manila has served as ADB's seat since 1966, the correct answer is Manila, Philippines.
A useful way to answer this question is to ask what each of these four cities is actually the headquarters of, since all four host some kind of international or regional office and it is easy to mix them up.
Once each city is matched to the organisation it actually hosts, only Manila lines up with the Asian Development Bank, distinguishing it clearly from the regional bodies and missions in the other three cities.
Therefore, the correct answer is Manila, Philippines.