To calculate \( \frac{4}{3} \times x \) when \( x = \frac{1}{6} \), substitute \( \frac{1}{6} \) for \( x \):
\[ \frac{4}{3} \times \frac{1}{6} = \frac{4 \times 1}{3 \times 6} = \frac{4}{18} \]
Now, simplify \( \frac{4}{18} \):
\[ \frac{4}{18} = \frac{2}{9} \]
Thus, \( \frac{4}{3} \times \frac{1}{6} = \frac{2}{9} \).