Given

$$\begin{gathered} \text{4096}\times \frac{2}{7}\times \frac{3}{4}=? \\ \Rightarrow \text{ 4096}\times \frac{6}{28}=? \end{gathered}$$

It can be approximated as

$$\begin{gathered} \begin{array}{l}\Rightarrow \text{ 4096}\times \frac{6}{30}=?\end{array} \\ \begin{array}{l}\Rightarrow \text{4096}\times \frac{1}{5}=?\\ \end{array} \\ \Rightarrow \text{\hspace{0.17em}?=}\frac{4096}{5}=819.2\approx 820 \end{gathered}$$

Hence, Option D is correct.