Answer
$Period = 4\pi $
See below
Work Step by Step
If B > 0, then the graphs of $y = \sec(Bx)$ and
$y = \csc(Bx)$ will have
$Period = \frac{2\pi}{B}$
For equation $y = 3 \csc \frac{1}{2}x$
$Period = \frac{2\pi}{\frac{1}{2}} = 4\pi $