To perform the division of fractions, take the reciprocal of 1/6:
[tex]\frac{6}{1}[/tex]Rememer that to divide by a fraction is the same that to multiply by its reciprocal. Then:
[tex]\begin{gathered} \frac{1}{3}\div\frac{1}{6}=\frac{1}{3}\times\frac{6}{1} \\ =\frac{1\times6}{3\times1} \\ =\frac{6}{3} \\ =2 \end{gathered}[/tex]Therefore:
[tex]\frac{1}{3}\div\frac{1}{6}=2[/tex]