1. **State the problem:** Evaluate the expression $$\frac{3}{4} \left( \frac{1}{3} + \frac{2}{7} \right)$$. 2. **Use the distributive property:** Multiply $$\frac{3}{4}$$ by the sum inside the parentheses. 3. **Add the fractions inside the parentheses:** $$\frac{1}{3} + \frac{2}{7} = \frac{1 \times 7}{3 \times 7} + \frac{2 \times 3}{7 \times 3} = \frac{7}{21} + \frac{6}{21} = \frac{7 + 6}{21} = \frac{13}{21}$$ 4. **Multiply:** $$\frac{3}{4} \times \frac{13}{21} = \frac{3 \times 13}{4 \times 21} = \frac{39}{84}$$ 5. **Simplify the fraction:** Find the greatest common divisor (GCD) of 39 and 84, which is 3. 6. **Cancel common factors:** $$\frac{\cancel{3} \times 13}{\cancel{3} \times 28} = \frac{13}{28}$$ 7. **Final answer:** $$\frac{13}{28}$$