A student was asked to find the value of
$$\left[\frac{4}{9} \div \left(\frac{3}{5} \div \frac{3}{2} \right)\times \frac{9}{25} \right] \times \frac{\left[\frac{2}{3} of \frac{4}{9} \div \left(3 \times \frac{3}{5} of \frac{4}{5}\right)\right]}{\frac{2}{3} \div \frac{3}{4} of \frac{5}{6}}$$ His answer was $$\frac{2}{9}$$.
What is the difference between his answer and the correct answer?

Expression : $$\left[\frac{4}{9} \div \left(\frac{3}{5} \div \frac{3}{2} \right)\times \frac{9}{25} \right] \times \frac{\left[\frac{2}{3} of \frac{4}{9} \div \left(3 \times \frac{3}{5} of \frac{4}{5}\right)\right]}{\frac{2}{3} \div \frac{3}{4} of \frac{5}{6}}$$

= $$\left[\frac{4}{9} \div \left(\frac{3}{5} \times \frac{2}{3} \right)\times \frac{9}{25} \right] \times \frac{\left[\frac{8}{27}\div \left(\frac{36}{25}\right)\right]}{\frac{2}{3} \div \frac{5}{8}}$$

= $$\left[\frac{4}{9} \times \frac{5}{2}\times \frac{9}{25} \right] \times \frac{\left[\frac{8}{27}\times \frac{25}{36}\right]}{\frac{2}{3} \times \frac{8}{5}}$$

= $$\frac{2}{5}\times\frac{\frac{50}{243}}{\frac{16}{15}}$$

= $$\frac{2}{5}\times\frac{50}{243}\times\frac{15}{16}$$

= $$\frac{25}{81\times4}=\frac{25}{324}$$