Chapter 4 - Section 4.2 - Amplitude, Reflection, and Period - 4.2 Problem Set - Page 203: 23

$12\pi$

We know that if $A$ is a real number and $B\gt0$, then the graphs of $y=Asin(Bx)$ and $y=Acos(Bx)$ will have an period of $\frac{2\pi}{B}$. Therefore, the period of the graph of $y=sin\frac{1}{6}x$ is $\frac{2\pi}{\frac{1}{6}}=2\pi\times6=12\pi$.