\(\Rightarrow y=8-\left(\frac{4}{3}\right)x\)

\(\Rightarrow y=4\times(2-\left(\frac{1}{3}\right)x)\)

for x intercept, \(y=0\)

\(0=4\times(2-\left(\frac{1}{3}\right)x)\)

\(\left(\frac{1}{3}\right)x=2\)

\(x=6\)

Volume generated by rotating the given region about x axis by washer method \(v=\int_{0}^{6}\pi[4\times(2-\left(\frac{1}{3}\right)x)]^{2}dx\)

\(v=\int_{0}^{6}16\pi[2^{2}-2\times2\left(\frac{1}{3}\right)x+(\left(\frac{1}{3}\right)x)^{2}]dx\)

\(v=\int_{0}^{6}16\pi[4-\left(\frac{4}{3}\right)x+\left(\frac{1}{9}\right)x^{2}]dx\)

\(v=\int_{0}^{6}16\pi[4x-\left(\frac{4}{3}\right)\left(\frac{1}{2}\right)x^{2}+\left(\frac{1}{9}\right)\left(\frac{1}{3}\right)x^{3}]\)

\(v=\int_{0}^{6}16\pi[4x-\left(\frac{2}{3}\right)x^{2}+\left(\frac{1}{27}\right)x^{3}]\)

\(v=16\pi[4\times6-\left(\frac{2}{3}\right)6^{2}+\left(\frac{1}{27}\right)6^{3}]-16\pi[4\times0-\left(\frac{2}{3}\right)0^{2}+\left(\frac{1}{27}\right)0^{3}]\)

\(v=16\pi[4\times6-\left(2\times\frac{36}{3}\right)+\left(\frac{216}{27}\right)]\)

\(v=16\pi[24-24+8]\)

\(v=128\pi\)

Volume \(=128\pi=402\)