d) \( \frac{3}{8}-\frac{5}{6} \div \frac{4}{3}+\frac{2}{9} \cdot \frac{27}{9} \)

Let's break down the expression step by step. 1. Start with the division \( \frac{5}{6} \div \frac{4}{3} \). To divide fractions, we multiply by the reciprocal: \[ \frac{5}{6} \div \frac{4}{3} = \frac{5}{6} \cdot \frac{3}{4} = \frac{15}{24} = \frac{5}{8} \] 2. Now, substitute that back into the expression and simplify: \[ \frac{3}{8} - \frac{5}{8} + \frac{2}{9} \cdot \frac{27}{9} \] 3. Next, calculate \( \frac{2}{9} \cdot \frac{27}{9} \): \[ \frac{2 \cdot 27}{9 \cdot 9} = \frac{54}{81} = \frac{2}{3} \] 4. Now, we substitute this into the expression: \[ \frac{3}{8} - \frac{5}{8} + \frac{2}{3} \] 5. Combine \( \frac{3}{8} - \frac{5}{8} \): \[ \frac{3 - 5}{8} = -\frac{2}{8} = -\frac{1}{4} \] 6. Thus, now we have: \[ -\frac{1}{4} + \frac{2}{3} \] 7. To add these fractions, we need a common denominator, which would be 12. Let's convert: \[ -\frac{1}{4} = -\frac{3}{12}, \quad \frac{2}{3} = \frac{8}{12} \] 8. Now add them together: \[ -\frac{3}{12} + \frac{8}{12} = \frac{5}{12} \] So, the final answer is: \[ \frac{5}{12} \]