Answer
$8\pi$
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 $y=sin\frac{1}{4}x$ is $\frac{2\pi}{\frac{1}{4}}=2\pi\times4=8\pi$.