The value of $$(6 - 3) \div \left[ (9 - 6) \div \left\{ (6 - 4) \div \left(2 + \frac{8}{13} \right) \right\} \right]$$​ is:

Correct option is B

Given:

​$$(6 - 3) \div \left[ (9 - 6) \div \left\{ (6 - 4) \div \left(2 + \frac{8}{13} \right) \right\} \right]$$​

Concept Used: 

$$\begin{array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\\hline \text{Brackets} &[],{}, () \\ \hline \text{Orders, of} & (power), √ (root) , of \\ \hline \text{Division}& ÷ \\ \hline \text{Multiplication} & × \\ \hline \text{Addition} & + \\ \hline \text{Subtraction} & - \\\hline \end{array}$$​

Solution:

$$= (6 - 3) \div \left[ (9 - 6) \div \left\{ (6 - 4) \div \left(2 + \frac{8}{13} \right) \right\} \right]\\ \ \\= (6 - 3) \div \left[ (9 - 6) \div \left\{ (6 - 4) \div \left( \frac{26+8}{13} \right) \right\} \right]\\ \ \\= (6 - 3) \div \left[ (9 - 6) \div \left\{ (6 - 4) \div \frac{34}{13} \right\} \right]\\ \ \\= (3) \div \left[ (3) \div \left\{ 2\times \frac{13}{34} \right\} \right]\\ \ \\= (3) \div \left[ (3) \times \frac{17}{13} \right]\\ \ \\= (3) \div \frac{51}{13}\\ \ \\= (3) \times \frac{13}{51}\\ \ \\= \frac{13}{17}$$​