To find an equivalent amount of flour for \( \frac{1}{3} \) of a cup, we can compare it to the options given:
- \( \frac{4}{12} \) of a cup: This simplifies to \( \frac{1}{3} \) of a cup because \( \frac{4}{12} = \frac{1}{3} \).
- \( \frac{4}{6} \) of a cup: This simplifies to \( \frac{2}{3} \) of a cup, which is not equivalent.
- \( \frac{1}{4} \) of a cup: This is not equivalent to \( \frac{1}{3} \).
- \( \frac{2}{3} \) of a cup: This is greater than \( \frac{1}{3} \) and not equivalent.
The only amount of flour that is equivalent to \( \frac{1}{3} \) of a cup in your list is \( \frac{4}{12} \) of a cup.