A student was asked to find the value of $$9\frac{4}{9}\div11\frac{1}{3} of \frac{1}{6} + \left(1\frac{1}{3} \times 1\frac{4}{5} \div \frac{3}{5}\right) \times 2\frac{1}{6} of \frac{2}{3} \div \frac{4}{3} of \frac{2}{3}$$. His answer was $$19\frac{1}{4}$$. What is the difference between his answer and the correct answer

$$9\frac{4}{9}\div11\frac{1}{3} of \frac{1}{6} + \left(1\frac{1}{3} \times 1\frac{4}{5} \div \frac{3}{5}\right) \times 2\frac{1}{6} of \frac{2}{3} \div \frac{4}{3} of \frac{2}{3}$$

$$\frac{85}{9}\div\frac{34}{3} of \frac{1}{6} + \left(\frac{4}{3} \times \frac{9}{5} \div \frac{3}{5}\right) \times \frac{13}{6} of \frac{2}{3} \div \frac{4}{3} of \frac{2}{3}$$
$$\frac{85}{9}\div\frac{34}{18}  + 4 \times \frac{13}{9} \div \frac{8}{9}$$

$$\frac{85}{9}\div\frac{34}{18} +  \frac{13}{2}$$ 

$$ 5\frac{13}{2} = \frac{23}{2}$$

Answer of the student = $$19\frac{1}{4} = \frac{77}{4}$$

Difference = $$\frac{77}{4} - \frac{23}{2} = \frac{31}{4} = 7\frac{3}{4}$$