To multiply the fractions \( \frac{2}{7} \) and \( \frac{2}{8} \), you multiply the numerators together and the denominators together:
\[ \frac{2}{7} \times \frac{2}{8} = \frac{2 \times 2}{7 \times 8} = \frac{4}{56} \]
Next, simplify \( \frac{4}{56} \). The greatest common divisor (GCD) of 4 and 56 is 4. So, divide both the numerator and the denominator by 4:
\[ \frac{4 \div 4}{56 \div 4} = \frac{1}{14} \]
Thus, \( \frac{2}{7} \times \frac{2}{8} = \frac{1}{14} \).