In the expansion of ${\left(2x+\frac{{\displaystyle 1}}{{\displaystyle 2x}}\right)}^6$, if the coefficient of $x^2$ is $\text{'}k\text{'}$ times the coefficient of $x^{-2}$, then $\text{'}k\text{'}$ equals

$T_{r+1}={}^6{C}_r{\left(2x\right)}^{6-r}\cdot \frac{1}{{\left(2x\right)}^r}$

$={}^6{C}_r{2}^{6-2r}\cdot x^{6-2r}$

If $\begin{array}{ll}6-2r=2& 6-2r=-2\\ 6-2=2r& 6+2=2r\\ 4=2r& 8=2r\\ \therefore r=2& \therefore r=4\end{array}$

Coefficient of $x^2=k$ coefficient of $x^{-2}$

$\therefore k=16$