What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y=12-x^2?

Area of rectangle: LxW

so

(2x) (y) = 2x (12-X^2)

then I would solve for x and substitute it back into the Area equation.

This is your area equation:

A = 2x (12-x^2)

maximize by differentiating and setting equal to 0 then solve for x.