You can factor the formula for the volume as
[tex]V = 4x^3-12x^2y+9xy^2 = x(2x-3y)^2[/tex]
So, your solid could be a prism. Its base is a square with side [tex]2x-3y[/tex] and height [tex]x[/tex].
So, its volume would be
[tex](2x-3y)\cdot (2x-3y) \cdot x = x(2x-3y)^2 = 4x^3-12x^2y+9xy^2[/tex]
