Answer
The difference quotient for the provided function is $4x+2h$.
Work Step by Step
Consider the provided function: $f\left( x \right)=2{{x}^{2}}$.
Now, substitute $x=x+h$ in the above equation to find $f\left( x+h \right)$
That is,
$f\left( x+h \right)=2{{\left( x+h \right)}^{2}}$
Now, apply the difference quotient formula,
$\begin{align}
& \frac{f\left( x+h \right)-f\left( x \right)}{h}=\frac{2{{\left( x+h \right)}^{2}}-2{{x}^{2}}}{h} \\
& =\frac{2{{x}^{2}}+4xh+2{{h}^{2}}-2{{x}^{2}}}{h} \\
& =\frac{h\left( 4x+2h \right)}{h} \\
& =4x+2h
\end{align}$
Hence, the difference quotient for the provided function is $4x+2h$.
