Question

Find a cubic function y = ax³ + bx² + cx + d whose graph has horizontal tangents at the points (-2,12) and (2,6).

Answer 1

You have four unknowns: a, b, c and d and therefore you will need 4 equations to solve for them. 
You are already given two points ON the curve: (-2, 12) and (2,6). Plug the numbers into the function and you have two equations. Then, ...
To find the slope, take the derivative of the function. "Horizontal tangent" means the slope at those points are zero.
Plug the x values of -2 and 2 and set the corresponding y' to zero and you will have two more equations. Solve the 4 simultaneous equations to find a, b, c and d.