Answer: Manila
Explanation: I believe this question is asking for the city with the greatest population in relation to their respective sizes.
<em>Delhi's area</em> = 573 <u>sq mi</u>
<em>Karachi's area</em> = 1,460 <u>sq mi</u>
<em>Manila's area</em> = 16.6 (rounded from 16.56) <u>sq mi</u>
<em>New York City's area</em> = 468.5 (rounded from 484) <u>sq mi</u>
*Manila is the smallest city of the four listed. Karachi is the biggest.*
Their <em>populations</em>, however, are as follows:
<em>Dehli </em>= 301,000
<em>Karachi </em>= 14.9 mil
<em>Manila </em>= 1.7 mil
<em>New York City</em> = 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.
<em>HOWEVER</em>
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)
<u>Delhi has the second-biggest area and lowest population count, so its pop. density is the smallest of all. Wrong answer.</u>
<u>New York has the biggest population density, but its the third-biggest city with the second-most population. This option is wrong.</u>
<u>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 </u><u><em>SMALLEST </em></u><u>city. This automatically is not an option. </u>
<u>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.</u>
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!