1. **Stating the problem:** Simplify the expression $$L = \frac{7}{6} \times \left(\frac{7}{2} - \frac{3}{2}\right)$$. 2. **Apply the subtraction inside the parentheses:** $$\frac{7}{2} - \frac{3}{2} = \frac{7 - 3}{2} = \frac{4}{2}$$ 3. **Rewrite the expression:** $$L = \frac{7}{6} \times \frac{4}{2}$$ 4. **Multiply the fractions:** $$L = \frac{7 \times 4}{6 \times 2} = \frac{28}{12}$$ 5. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor (4):** $$L = \frac{\cancel{28}^{7 \times 4}}{\cancel{12}^{3 \times 4}} = \frac{7}{3}$$ 6. **Final answer:** $$L = \frac{7}{3}$$