Given,

$\frac{4}{5}\times \frac{3}{7}÷\frac{6}{7}÷\frac{5}{9}=?$

It can also be written as

$$\begin{gathered} = \frac{4}{5}\times \frac{3}{7}÷\frac{6}{7}÷\frac{5}{9} \\ =\frac{4}{5}\times \frac{3}{7}\times \frac{7}{6}\times \frac{9}{5} \\ =\frac{4}{5}\times \frac{1}{2}\times \frac{5}{9} \\ = \frac{2}{5}\times \frac{9}{5} \\ =\frac{18}{25} \end{gathered}$$

Hence, Option C is correct.