1. **State the problem:** Simplify the expression $$\left(\frac{27}{8}\right) \times \left(-\frac{4}{3}\right)$$. 2. **Recall the rule for multiplying fractions:** Multiply the numerators together and the denominators together. 3. **Multiply the numerators:** $$27 \times (-4) = -108$$. 4. **Multiply the denominators:** $$8 \times 3 = 24$$. 5. **Write the fraction:** $$\frac{-108}{24}$$. 6. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD), which is 12:** $$\frac{\cancel{108}^{9}}{\cancel{24}^{2}} = \frac{-9}{2}$$. 7. **Final answer:** $$-\frac{9}{2}$$ or $$-4.5$$.