Actually the slope of the perpendicular would be -1/2, giving you
y = (-1/2)x + b through the point (4,6)
substituting, we get 6 = (-1/2)4 + b, which simplifies to 6 = -2 + b, or 8 = b
The final equation would be y = (-1/2)x + 8, which is answer D.
Another way to approach this is to plug the number 4 into each of the answer choices, and see which equation yields 6 for y:
A gives you 6
B gives you 2
C gives you 4
D gives you 6
So you can eliminate B&C, and since a perpendicular is the negative inverse of the original it has to be D
Hope this helps!