$\sqrt[4]{12}\times \sqrt[7]{6}$  can be simplified as:

It is given that the mathematical expression is $\sqrt[4]{12}\times \sqrt[7]{6}$_.
$\begin{array}{l}\sqrt[4]{12}\times \sqrt[7]{6}={\left(12\right)}^{\frac{1}{4}}\times {\left(6\right)}^{\frac{1}{7}}\\ ={\left(2\times 2\times 3\right)}^{\frac{1}{4}}\times {\left(2\times 3\right)}^{\frac{1}{7}}\\ =2^{\frac{1}{4}}\cdot 2^{\frac{1}{4}}\cdot 3^{\frac{1}{4}}\cdot 2^{\frac{1}{7}}\cdot 3^{\frac{1}{7}}\end{array}$ 
$\begin{array}{l}=2^{\left(\frac{1}{4}+\frac{1}{4}+\frac{1}{7}\right)}\times 3^{\left(\frac{1}{4}+\frac{1}{7}\right)}\\ =2^{\frac{18}{28}}\times 3^{\frac{11}{28}}\\ =\sqrt[28]{2^{18}}\times \sqrt[28]{3^{11}}\\ =\sqrt[28]{2^{18}\times 3^{11}}\end{array}$ 
Therefore, the correct answer is $\sqrt[\mathbf{28}]{{\mathbf{2}}^{\mathbf{18}}\mathbf{\times }{\mathbf{3}}^{\mathbf{11}}}$.