1. **State the problem:** Calculate the value of $$\left(\frac{1}{3} + \frac{1}{5} \div \frac{1}{8}\right) \times \frac{1}{6}$$. 2. **Recall the order of operations:** Division and multiplication are performed before addition unless parentheses indicate otherwise. 3. **Evaluate the division inside the parentheses first:** $$\frac{1}{5} \div \frac{1}{8} = \frac{1}{5} \times \frac{8}{1} = \frac{8}{5}$$ 4. **Rewrite the expression:** $$\left(\frac{1}{3} + \frac{8}{5}\right) \times \frac{1}{6}$$ 5. **Find a common denominator to add the fractions inside the parentheses:** The common denominator of 3 and 5 is 15. $$\frac{1}{3} = \frac{5}{15}, \quad \frac{8}{5} = \frac{24}{15}$$ 6. **Add the fractions:** $$\frac{5}{15} + \frac{24}{15} = \frac{29}{15}$$ 7. **Multiply by $$\frac{1}{6}$$:** $$\frac{29}{15} \times \frac{1}{6} = \frac{29}{90}$$ 8. **Final answer:** $$\boxed{\frac{29}{90}}$$