we want the volume the green volume as the picture shows us

the function is $\displaystyle y^2=8x $

$\displaystyle y = \sqrt{8x} $

to make it easier let new x=x+4 to make the volume around the y-axis

so the new question will be

$\displaystyle y^2 = 8(x+4) $ and x=-2 around the y-axis

so the picture will be like this

and we want the volume revolution around y-axis

note that $\displaystyle y = \sqrt{8(x+4)} $ is not all the curve if we calculate the volume for y it will be half of what we need since it is symmetric

see this

the volume of this around y-axis

$\displaystyle \int _{-4}^{-2} 2\pi x \sqrt{8(x+4)} dx $

multiply it with 2 to get what you need

any questions