center of circle: (-4,2)
Using the point slope equation and the fact that perpendicular lines are negative reciprocals of each other.
y - 2 = (-1/2)(x+4)
2y - 4 = -x - 4
2y = -x
Since the equation above is the equation of the line perpendicular to y=2x+2, we can find the point of intersection
4x + 4 = -x
4x + x = -4
Subtstituting x in the give equation you get,
Using the distance formula you get the radius of the circle.