Since $\frac{1}{3}$ of $x$ is equal to 4, then $x$ is equal to $3 \times 4$ or 12. Thus, $\frac{1}{6}$ of $x$ is equal to $12 \div 6=2$. Alternatively, since $\frac{1}{6}$ is one-half of $\frac{1}{3}$, then $\frac{1}{6}$ of $x$ is equal to one-half of $\frac{1}{3}$ of $x$, which is $4 \div 2$ or 2.