Answer
The period of the graph will be $4$.
Work Step by Step
The given graph shows the function of:
$y=\cos{\frac{\pi}{2}{x}}$
As shown in the cosine graph, the period of the $\cos{x}$ graph is $2\pi$
The graph of $\cos{x}$ is compressed by $\frac{\pi}{2}$, so the new period is:
$\frac{2\pi}{\frac{\pi}{2}}=4$
