To find the product of \(\frac{2}{3}\) and \(\frac{5}{9}\), you multiply the numerators together and the denominators together:
\[ \frac{2}{3} \times \frac{5}{9} = \frac{2 \times 5}{3 \times 9} = \frac{10}{27} \]
So, the product of \(\frac{2}{3} \times \frac{5}{9}\) is \(\frac{10}{27}\).