Find the Equation of the Plane Tangent to the Surface S

Difficult

Let $S = \{ (x,y,z) \in \mathbb{R} | x^2 + y^2 + z^2 = 16 \; \text{and} \; x^2+y^2 \geq 4 \}$. Find the equation of the plane tangent to the surface $S$ at the point $P = (\sqrt{6}, \sqrt{6}, 2)$.