1. **State the problem:** We need to compare the fractions $\frac{2}{3}$ and $\frac{4}{7}$ to determine which is larger. 2. **Compare the fractions:** To compare fractions, we find a common denominator or cross-multiply. 3. **Cross-multiply:** $$2 \times 7 = 14$$ $$4 \times 3 = 12$$ Since $14 > 12$, $\frac{2}{3}$ is larger than $\frac{4}{7}$. 4. **Find how much larger:** Subtract the smaller fraction from the larger: $$\frac{2}{3} - \frac{4}{7}$$ 5. **Find common denominator:** The least common denominator of 3 and 7 is 21. 6. **Rewrite fractions:** $$\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}$$ $$\frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21}$$ 7. **Subtract:** $$\frac{14}{21} - \frac{12}{21} = \frac{14 - 12}{21} = \frac{2}{21}$$ 8. **Simplify:** $\frac{2}{21}$ is already in simplest form. **Final answer:** $\frac{2}{3}$ is larger than $\frac{4}{7}$ by $\frac{2}{21}$.