FOLLOW BODMAS rule to solve this question, as per the given order below.

Step 1: Parts of the equation enclosed in ‘Brackets’ must be solved first.

Step 2: An mathematical ‘Of’ or ‘Exponent’ must be solved next.

Step 3: Next, the parts of the equation containing ‘Division’ or ‘Multiplication’ are calculated.

Step 4: Last but not the least, the parts of the equation containing ‘Addition’ or ‘Subtraction’ are calculated.

Given,

$(\BEGIN{array}{l} \frac{{56}}{{135}} \div \left\{ {\left( {\frac{7}{3} + \frac{1}{5}} \right) \div \left( {9 + 3\frac{3}{4}} \right) \times \frac{{17}}{{19}}} \right\} = \frac{1}{?}\\ \Rightarrow \frac{{56}}{{135}} \div \left\{ {\left( {\frac{7}{3} + \frac{1}{5}} \right) \div \left( {9 + \frac{{15}}{4}} \right) \times \frac{{17}}{{19}}} \right\} = \frac{1}{?}\\ \Rightarrow \frac{{56}}{{135}} \div \left\{ {\frac{{38}}{{15}} \div \frac{{51}}{4} \times \frac{{17}}{{19}}} \right\} = \frac{1}{?} \end{array})$

$(\begin{array}{l} \Rightarrow \frac{{56}}{{135}} \div \left\{ {\frac{{38}}{{15}} \times \frac{4}{{51}} \times \frac{{17}}{{19}}} \right\} = \frac{1}{?}\\ \Rightarrow \frac{{56}}{{135}} \div \frac{8}{{45}} = \frac{1}{?}\\ \Rightarrow \frac{{56}}{{135}} \times \frac{{45}}{8} = \frac{1}{?}\\ \Rightarrow \frac{7}{3} = \frac{1}{?} \end{array})$