1. **State the problem:** Multiply and simplify the expression $$\frac{12x - 8}{9} \times \frac{6}{2 - 3x}$$. 2. **Write the expression:** $$\frac{12x - 8}{9} \times \frac{6}{2 - 3x}$$ 3. **Factor where possible:** Factor numerator $12x - 8$: $$12x - 8 = 4(3x - 2)$$ Rewrite denominator $2 - 3x$ as $-(3x - 2)$ to match the factor: $$2 - 3x = -(3x - 2)$$ 4. **Substitute factored forms:** $$\frac{4(3x - 2)}{9} \times \frac{6}{-(3x - 2)}$$ 5. **Multiply numerators and denominators:** $$\frac{4(3x - 2) \times 6}{9 \times -(3x - 2)} = \frac{24(3x - 2)}{-9(3x - 2)}$$ 6. **Cancel common factors:** $$\frac{24\cancel{(3x - 2)}}{-9\cancel{(3x - 2)}}$$ 7. **Simplify the fraction:** $$\frac{24}{-9} = -\frac{24}{9}$$ 8. **Reduce the fraction by dividing numerator and denominator by 3:** $$\frac{\cancel{24}^8}{\cancel{9}^3}$$ 9. **Final simplified answer:** $$-\frac{8}{3}$$