Answer
False; $\frac{d}{dx}(4f(x) + x^3) |_{x=2} \neq 20$.
Work Step by Step
The error in this example occurs when the writer evaluates $x^3$ at $x=2$ before differentiating. Correct answer:
If $f'(2) = 5$, then
\begin{align}
& \frac{d}{dx}(4f(x) + x^3) |_{x=2} \\
&= 4f'(x) + 3x^2 |_{x=2} \\
&= 4f'(2) + 3(4) \\
&= 4(5) + 12 \\
&= 32 \\
\end{align}