To multiply the fractions \( \frac{1}{4} \) and \( \frac{2}{3} \), you can multiply the numerators together and the denominators together:
\[ \frac{1 \times 2}{4 \times 3} = \frac{2}{12} \]
Next, simplify \( \frac{2}{12} \):
\[ \frac{2}{12} = \frac{1}{6} \]
So, \( \frac{1}{4} \times \frac{2}{3} = \frac{1}{6} \).