Answer
$\dfrac{4}{3}$
Work Step by Step
Volume of a rectangular box is given by $V=xyz$
From the given question, we have
$x=6-2y-3z$
Thus, $V=6yz-2y^2z-3yz^2$
This gives $V_y=6z-4yz-3z^2, V_z=6y-2y^2-6yz$
After solving, we get
$y=1,z=\dfrac{2}{3}$
and $x=6-2y-3z=2$
Hence, the volume of a rectangular box will be $V=xyz=(2)(1)(\dfrac{2}{3})=\dfrac{4}{3} $
