1. **State the problem:** Evaluate the expression $$\frac{4}{3} \div \left( \frac{11}{12} - \frac{9}{8} \right)$$ and write the answer as a fraction or mixed number in simplest form. 2. **Recall the formula and rules:** Division of fractions is done by multiplying by the reciprocal. That is, $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$. 3. **Calculate the expression inside the parentheses:** $$\frac{11}{12} - \frac{9}{8} = \frac{11 \times 2}{12 \times 2} - \frac{9 \times 3}{8 \times 3} = \frac{22}{24} - \frac{27}{24} = \frac{22 - 27}{24} = \frac{-5}{24}$$ 4. **Rewrite the original expression:** $$\frac{4}{3} \div \left( \frac{-5}{24} \right) = \frac{4}{3} \times \frac{24}{-5}$$ 5. **Multiply the fractions:** $$\frac{4}{3} \times \frac{24}{-5} = \frac{4 \times 24}{3 \times -5} = \frac{96}{-15}$$ 6. **Simplify the fraction:** $$\frac{\cancel{96}^{32}}{\cancel{15}^{5}} = \frac{32}{-5} = -\frac{32}{5}$$ 7. **Convert to mixed number:** $$-\frac{32}{5} = -6 \frac{2}{5}$$ **Final answer:** $$-6 \frac{2}{5}$$