In the problem the center of dilation is located at (0, 0).
The problem whats us to find the image of the point D given that it has a scale factor of 1/2 of C.
Since we can stablish that the points of the D is just 1/2 of the points of C.
C has the coordinate (0, 4).
And (1/2)(0) = 0
(1/2)(4) = 2
Therefore the coordinates of D which is half of C is (0, 2)
Which is LETTER B. (0, 2)