Answer
$\color{blue}{8}$
Work Step by Step
$\begin{align*}
E(3X-4) &= 3E(X) - 4 & [\ \text{Corollary 3.5.1, p. 148}\ ] \\
&= 3\left(10\cdot \frac{2}{5}\right) - 4 & [\ \text{Theorem 3.5.1, p. 139,} \\
& & \; X\sim\text{Binomial}(n=10,p=2/5) \implies \\
&& E(X) = np = (10)(2/5) \ ] \\
&= 12 -4 \\
\color{blue}{E(3X-4)}\ &\color{blue}{= 8}
\end{align*}$