1. **State the problem:** We need to divide the fraction $\frac{5}{6}$ by the fraction $\frac{4}{3}$. This is written as $\frac{5}{6} \div \frac{4}{3}$.\n\n2. **Recall the rule for dividing fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $\frac{4}{3}$ is $\frac{3}{4}$. So,\n$$\frac{5}{6} \div \frac{4}{3} = \frac{5}{6} \times \frac{3}{4}.$$\n\n3. **Multiply the numerators and denominators:**\n$$\frac{5 \times 3}{6 \times 4} = \frac{15}{24}.$$\n\n4. **Simplify the fraction:** Both numerator and denominator can be divided by 3.\n$$\frac{\cancel{15}^{5} }{\cancel{24}^{8}} = \frac{5}{8}.$$\n\n5. **Final answer:**\n$$\frac{5}{6} \div \frac{4}{3} = \frac{5}{8}.$$\nThis means when you divide $\frac{5}{6}$ by $\frac{4}{3}$, the result is $\frac{5}{8}$.