Must 'complete the square', so get x's on right side by themselves by subtracting 16 to left side.
y-16 = 2x^2 - 12x
Factor out the 2 on the right side of equation.
y-16 = 2(x^2-6x)
Now you have to 'complete the square' on the right side of the equation. When you add the 9 on the right side, be careful adding to the left side, because there is a 2 outside of the parenthesis on the right side. Now, you add (9*2)=18 onto the left side of the equation.
You have your perfect square, which is (x-3)^2
Now subtract 2 to the right side of the equation to put it into vertex form.
Answer is C.
Let me know if you have any questions :). This can be a rather difficult concept.