Since none of the options make sense with 23, I assume it was a typo, and you meant 2/3.
Let l,w and h be the length, width and height of the original prism, and l',w' and h' be the length, width and height of the new prism. We are given
[tex] l' = l\times \cfrac{2}{3},\quad w' = w\times \cfrac{2}{3},\quad h' = h\times \cfrac{2}{3} [/tex]
Also, if we call V the original volume, and V' the volume of the new prism, we have
[tex] V = lhw,\quad V'=l'h'w' [/tex]
Substitute the expressions for l', h' and w' in the formula for V':
[tex] V'=l'h'w' = l\times \cfrac{2}{3}\times w\times \cfrac{2}{3}\times h\times \cfrac{2}{3} = l\times h \times w \times \cfrac{2}{3}\times\cfrac{2}{3}\times\cfrac{2}{3} = V \times \left(\cfrac{2}{3}\right)^3 = V\times\cfrac{8}{27} [/tex]
