1. **State the problem:** Multiply the fractions $\frac{2}{3}$ and $\frac{7}{9}$. 2. **Formula for multiplying fractions:** To multiply two fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. **Apply the formula:** $$\frac{2}{3} \times \frac{7}{9} = \frac{2 \times 7}{3 \times 9} = \frac{14}{27}$$ 4. **Simplify the fraction if possible:** Check if 14 and 27 have any common factors other than 1. Since they do not, the fraction is already in simplest form. 5. **Final answer:** $$\frac{2}{3} \times \frac{7}{9} = \frac{14}{27}$$