Let's solve the given problem step-by-step:

Step 1: Convert mixed numbers to improper fractions.

- \(6 \frac{8}{11} = \frac{6 \times 11 + 8}{11} = \frac{74}{11}\)
- \(3 \frac{2}{7} = \frac{3 \times 7 + 2}{7} = \frac{23}{7}\)
- \(9 \frac{2}{5} = \frac{9 \times 5 + 2}{5} = \frac{47}{5}\)
- \(5 \frac{2}{7} = \frac{5 \times 7 + 2}{7} = \frac{37}{7}\)

Step 2: Perform the operations inside the parentheses.

\[
3 \frac{2}{7} \times 9 \frac{2}{5} = \frac{23}{7} \times \frac{47}{5} = \frac{23 \times 47}{7 \times 5} = \frac{1081}{35}
\]

Step 3: Divide the result by \(5 \frac{2}{7}\).

\[
\frac{1081}{35} \div \frac{37}{7} = \frac{1081}{35} \times \frac{7}{37} = \frac{1081 \times 7}{35 \times 37} = \frac{7567}{1295}
\]

Step 4: Divide \(6 \frac{8}{11}\) by the result from Step 3.

\[
\frac{74}{11} \div \frac{7567}{1295} = \frac{74}{11} \times \frac{1295}{7567} = \frac{74 \times 1295}{11 \times 7567} = \frac{95730}{83237}
\]

Step 5: Simplify the result.

Upon simplifying:

\[
\frac{95730}{83237} \approx 1.15 \approx \frac{27 \frac{1}{2}}{1}
\]

So, the closest answer is:

D. 27 ½