To divide fractions, you multiply by the reciprocal of the divisor.
First, let's express the problem:
\[ \frac{4}{9} \div \frac{2}{3} \]
To divide by \(\frac{2}{3}\), we multiply by its reciprocal:
\[ \frac{4}{9} \times \frac{3}{2} \]
Now, multiply the numerators and the denominators:
\[ = \frac{4 \times 3}{9 \times 2} = \frac{12}{18} \]
Next, we simplify \(\frac{12}{18}\) by finding the greatest common divisor (GCD) of 12 and 18, which is 6:
\[ \frac{12 \div 6}{18 \div 6} = \frac{2}{3} \]
So, the result of \( \frac{4}{9} \div \frac{2}{3} \) is:
\[ \frac{2}{3} \]