According to the formula, If pipe A  and B fills a tank in x and y hours respectively, but a third pipe C empties the full tank in z hours then the net portion filled in 1 hour when all of them are opened together is $\frac{\mathrm{xyz}}{\mathrm{yz}+\mathrm{xz}-\mathrm{xy}}$ hours.

So,

 $$\begin{gathered} \frac{4\times 6\times 8}{(4\times 8)+(6\times 8)-(4\times 6)} \\ =\frac{4\times 6\times 8}{56}=\frac{24}{7} \mathrm{or} 3\frac{3}{7}\mathrm{hours} \end{gathered}$$

Therefore, the tank will be filled in $3\frac{3}{7}$ hours when all the pipes are opened simultaneously.

Hence option A is correct.