Answer
Please see below.
Work Step by Step
Please note that the absolute value for sine and cosine removes the lower half of the graph, which is below the $x$-axis, and flips it above. This results in two complete cycles, where there had been one.
So, since the period of $2\sin \frac{\pi x }{2}$ is $\frac{2\pi }{\frac{\pi }{2}}=4$, the period of $y=- \left |2 \sin \frac{ \pi x}{2} \right |$ will become $\frac{4 }{2}=2$.
