To divide fractions, you can multiply the first fraction by the reciprocal of the second fraction.
So, to divide \( \frac{4}{5} \) by \( \frac{2}{3} \):
\[ \frac{4}{5} \div \frac{2}{3} = \frac{4}{5} \times \frac{3}{2} \]
Now multiply the numerators and the denominators:
\[ = \frac{4 \times 3}{5 \times 2} = \frac{12}{10} \]
Now, simplify \( \frac{12}{10} \):
\[ = \frac{6}{5} \quad \text{(by dividing both the numerator and denominator by 2)} \]
So, \( \frac{4}{5} \div \frac{2}{3} = \frac{6}{5} \) or \( 1 \frac{1}{5} \) as a mixed number.