To multiply the fractions \( \frac{2}{3} \) and \( \frac{6}{7} \), you multiply the numerators together and the denominators together:
\[ \frac{2}{3} \times \frac{6}{7} = \frac{2 \times 6}{3 \times 7} = \frac{12}{21} \]
Now, we can simplify \( \frac{12}{21} \) by finding the greatest common divisor (GCD) of 12 and 21, which is 3:
\[ \frac{12 \div 3}{21 \div 3} = \frac{4}{7} \]
So,
\[ \frac{2}{3} \times \frac{6}{7} = \frac{4}{7} \]