1. Stating the problem: Simplify the expression $\frac{2}{3} - \frac{3}{7}$.\n\n2. To subtract fractions, they must have a common denominator. The denominators here are 3 and 7.\n\n3. Find the least common denominator (LCD) of 3 and 7, which is $3 \times 7 = 21$.\n\n4. Convert each fraction to an equivalent fraction with denominator 21:\n$$\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}$$\n$$\frac{3}{7} = \frac{3 \times 3}{7 \times 3} = \frac{9}{21}$$\n\n5. Now subtract the numerators while keeping the denominator the same:\n$$\frac{14}{21} - \frac{9}{21} = \frac{14 - 9}{21} = \frac{5}{21}$$\n\n6. The fraction $\frac{5}{21}$ cannot be simplified further because 5 and 21 have no common factors other than 1.\n\nFinal answer: $$\frac{2}{3} - \frac{3}{7} = \frac{5}{21}$$