2022 TWO(d)

A rectangle has one vertex at $(0,0)$ and the opposite vertex on the curve $y=6e^{1-0.5x}$, where $x>0$, as
shown on the graph below.

Find the maximum possible area of the rectangle.

*You must use calculus and show any derivatives that you need to find when solving this problem.*

*You do not have to prove that the area you have found is a maximum.*