The teacher will be very surprised to see your correct solution 😉
3*y2 + 3*z2 + 6*x2 - 4*x*y - 2*y*z + 4*x*z = 0
-4*x*y + 4*x*z + 6*x2 - 2*y*z + 3*y2 + 3*z2 = 0