Answer
$\dfrac{32 \pi}{3} \ cubic \ units $
Work Step by Step
The volume of a solid generated by revolving region $R$ about x-axis can be calculated by using Washer Method as:
The volume of revolution of the curve can be expressed as: $V=\pi \int_p^q [f(x)^2- g(x)^2] dx\\=\pi \int_{0}^{4} 4x dx -\pi \int_0^4 x^2 dx \\=(4) (\pi) [\dfrac{x^2}{2}]_0^4 -\pi [\dfrac{x^3}{4}]_0^4\\=\pi ((2)(16)-\dfrac{4^3}{3}) \\=\dfrac{32 \pi}{3} \ cubic \ units $
