Manila
Explanation: I believe this question is asking for the city with the greatest population in relation to their respective sizes.
Delhi's area = 573 sq mi
Karachi's area = 1,460 sq mi
Manila's area = 16.6 (rounded from 16.56) sq mi
New York City's area = 468.5 (rounded from 484) sq mi
*Manila is the smallest city of the four listed. Karachi is the biggest.*
Their populations, however, are as follows:
Dehli = 301,000
Karachi = 14.9 mil
Manila = 1.7 mil
New York City = 8.3 mil
*Karachi has the most people of the four listed. Delhi has the least.*
Karachi has the largest population listed, but has the largest area as well, so that's not it.
New York City's got a pretty big population size, the second-largest actually, but the area of New York City is the third-largest of the cities listed. Wrong.
Delhi's pretty sizable as well, being the second biggest city listed, but the population count is the lowest of all.
Manila has the third-highest population count, and is the smallest city listed. I think this is your best option.
HOWEVER
I might have answered this question wrong, since the question was phrased weirdly, so we'll also try the Population Density method to see what answer we come up with.
So:
Delhi:
301,000/573 = 525.3 (rounded)
Karachi:
14,900,000/1,460 = 10205.5 (rounded)
Manila:
1,700,000/16.6 = 102409.6 (rounded)
New York City:
8,300,000/468.5 = 17716.1 (rounded)
Delhi has the second-biggest area and lowest population count, so its pop. density is the smallest of all. Wrong answer.
New York has the biggest population density, but its the third-biggest city with the second-most population. This option is wrong.
Karachi has the third-biggest population density, and it is the most populated and biggest city of the four, but we're looking for the SMALLEST city. This automatically is not an option.
Manila has the second-largest population density (with NYC having the largest) with the third-largest population count and is the smallest city of all.
So from both methods, I've come to the conclusion that Manila is the answer. Hopefully I'm right, and I hope this helped. :) If you need help understanding anything, let me know!