1. **State the problem:** We need to solve the expression $$0.5 \times \frac{7}{6} - \frac{11}{8}$$. 2. **Recall the rules:** Multiplication and subtraction of fractions require a common denominator for subtraction, and multiplication is straightforward. 3. **Multiply 0.5 by \frac{7}{6}:** $$0.5 \times \frac{7}{6} = \frac{1}{2} \times \frac{7}{6} = \frac{1 \times 7}{2 \times 6} = \frac{7}{12}$$ 4. **Rewrite the expression:** $$\frac{7}{12} - \frac{11}{8}$$ 5. **Find a common denominator:** The least common denominator of 12 and 8 is 24. 6. **Convert fractions to have denominator 24:** $$\frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24}$$ $$\frac{11}{8} = \frac{11 \times 3}{8 \times 3} = \frac{33}{24}$$ 7. **Subtract the fractions:** $$\frac{14}{24} - \frac{33}{24} = \frac{14 - 33}{24} = \frac{-19}{24}$$ 8. **Final answer:** $$\boxed{\frac{-19}{24}}$$