To multiply the fractions \( \frac{5}{6} \) and \( \frac{4}{6} \), you multiply the numerators together and the denominators together:
\[ \frac{5}{6} \times \frac{4}{6} = \frac{5 \times 4}{6 \times 6} = \frac{20}{36} \]
Next, simplify the fraction \( \frac{20}{36} \). Both the numerator and the denominator can be divided by 4:
\[ \frac{20 \div 4}{36 \div 4} = \frac{5}{9} \]
So, \( \frac{5}{6} \times \frac{4}{6} = \frac{5}{9} \).