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Is the diagram visible? and also open up the "spoiler"

Let M be the center of square ABCD. Then, M is the midpoint of both AC and BD.
We can find coordinates of M as follows:
. M is midpoint of AC --> x(M) = (-6+4)/2; y(M) = (0+2)/2 or M(-1,1)
. M is midpoint of BD --> x(B) = (2xM - xD) = -2-0 = -2; y(B) = (2yM - yD) = 2-(-4) = 6
Finally, we get B(-2,6) --> C

Checking options is the best way out

By visualizing options and coordinates in diagram answer is C.

Different view, and great.

One more method:

1) We know the line connecting B and D is perpendicular to the line connecting A and C, so the slope of line B-->D will be the reciprocal of slope of A-->C
2) slope of A-->C = (2-0)/(4+6) = 1/5
3) slope of B-->D = negative reciprocal of 1/5, therefore = -5
4) Now for B-->D we have y = -5x - 4, since coordinates of D are (0, -4)
5) Check answers to see which fits our line. From the figure and the fact that ABCD is a square, we know coordinates of B will be (x, y) where x<0 and y>0, so cross out answer choices D and E
6) In this case, 6 = (-5)*(-2) - 4, so answer is C

Given Coordinate points:
A(-6,0)
B(x,y)
C(4,2)
D(0,-4)

Take Mid points of AC and BD
AC: (-6+4)/2 and (0+2)/2
AC: (-2/2) and (2/2)
(x,y) of AC are (-1,1)

Now take Mid points of BD
BD: (x+0)/2 and (y-4)/2
BD: x/2 and (y-4)/2

Compare with each other:
(x,y) of AC are (-1,1) and (x,y) of BD are (x/2,(y-4)/2)

x/2=-1 and (y-4)/2=1
x=-2 and y=6

So coordinates of B are (-2,6) Option C

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