The Area of the rectangle is $\displaystyle A(x)=Base*Height=6x\cos(x)$
Are we supposed to find the value of x that maximizes the area?
Thus, $\displaystyle \frac{dA}{dx}=-6x\sin(x)+6\cos(x)$
Setting this equal to zero, we get that $\displaystyle \cot(x)=x$. Using your calculator, we see that this is the case for $\displaystyle x=\pm.86 \ x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$
We take the positive value.
Thus, the area of the rectangle is $\displaystyle A(.86)=6(.86)\cos(.86)\approx \color{red}\boxed{3.37}$.
I believe this is the answer.
Hope that this makes sense to you!
--Chris