We know that y varies directly with x to the power of 3, which means that we can express y as:
[tex]y=kx^3[/tex]
where k is the constant of proportionality. To determine the value of k we plug y=6 and x=2 in the expression above and solve the resulting expression:
[tex]\begin{gathered} 6=k(2)\placeholder{⬚}^3 \\ 8k=6 \\ k=\frac{6}{8} \\ k=\frac{3}{4} \end{gathered}[/tex]
Hence the value of k is 3/4 and the expression for y is:
[tex]y=\frac{3}{4}x^3[/tex]
Plugging x=4 we have that:
[tex]\begin{gathered} y=\frac{3}{4}(4)\placeholder{⬚}^3 \\ y=\frac{3}{4}(64) \\ y=48 \end{gathered}[/tex]
Therefore, when x=4 the value of y is 48.
