1. The problem is to solve the division of two fractions: $\frac{2}{3} \div \frac{6}{9}$.\n\n2. The formula for dividing fractions is: \n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$\nThis means we multiply the first fraction by the reciprocal of the second fraction.\n\n3. Applying the formula: \n$$\frac{2}{3} \div \frac{6}{9} = \frac{2}{3} \times \frac{9}{6}$$\n\n4. Multiply the numerators and denominators: \n$$\frac{2 \times 9}{3 \times 6} = \frac{18}{18}$$\n\n5. Simplify the fraction by canceling common factors: \n$$\frac{\cancel{18}}{\cancel{18}} = 1$$\n\n6. Therefore, the final answer is: \n$$1$$