Answer
The difference quotient for the provided function is $4$.
Work Step by Step
Consider the provided function: $f\left( x \right)=4x$.
Now, substitute $x=x+h$ in the above equation to find $f\left( x+h \right)$
That is,
$f\left( x+h \right)=4\left( x+h \right)$
Now, apply the difference quotient formula,
$\begin{align}
& \frac{f\left( x+h \right)-f\left( x \right)}{h}=\frac{4\left( x+h \right)-4x}{h} \\
& =\frac{4x+4h-4x}{h} \\
& =\frac{4h}{h} \\
& =4
\end{align}$
Hence, the difference quotient for the provided function is $4$
