The equation of the plane looks odd. I'm guessing that it should actually be .

The centre C of the sphere must lie on the line L, so for some value of . Also, the distance from C to the plane must be 4. The formula for the distance from the point to the plane is . Plug the coordinates of C and the coefficients of the equation of the plane into that formula, set it equal to 4, and you have an equation for the two values of . You then know the coordinates of C, and the rest is easy.