1. **State the problem:** We need to find the result of dividing $\frac{2}{3}$ by $\frac{2}{7}$. 2. **Recall the division of fractions rule:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{2}{3} \div \frac{2}{7} = \frac{2}{3} \times \frac{7}{2}$$ 3. **Multiply the numerators and denominators:** $$\frac{2 \times 7}{3 \times 2} = \frac{14}{6}$$ 4. **Simplify the fraction:** Both numerator and denominator share a common factor of 2. $$\frac{\cancel{14}^{7}}{\cancel{6}^{3}} = \frac{7}{3}$$ 5. **Final answer:** $$\frac{2}{3} \div \frac{2}{7} = \frac{7}{3}$$