Answer
$\frac{\pi}{3}$
Work Step by Step
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 $y=cos6x$ is $\frac{2\pi}{6}=\frac{2\pi\div2}{6\div2}=\frac{\pi}{3}$.