To divide fractions, you multiply the first fraction by the reciprocal (or inverse) of the second fraction.
So, you have:
\[ \frac{2}{5} \div \frac{2}{3} = \frac{2}{5} \times \frac{3}{2} \]
Now, multiply the fractions:
\[ \frac{2 \times 3}{5 \times 2} = \frac{6}{10} \]
Now, simplify \(\frac{6}{10}\):
\[ \frac{6}{10} = \frac{3}{5} \]
Therefore:
\[ \frac{2}{5} \div \frac{2}{3} = \frac{3}{5} \]