Answer
$Period =\frac{\pi}{4}$
See below
Work Step by Step
If C is any real number and B > 0, then the graphs of $y = tan (Bx + C)$ and
$y = cot (Bx + C)$ will have
$Period = \frac{\pi}{B}$
$Horizontal\ shift = \frac{-C}{B}$
For equation $y = \cot 4x$
$Period = \frac{\pi}{4}$
Some values
$y = 0, at\ x = \frac{\pi}{8}$
$y = 1\ at\ x = \frac{\pi}{16}$
$y = -1\ at\ x = \frac{3\pi}{16}$
$y -> \pm \infty\ at\ x = 0, \frac{\pi}{4}$
Using graph of $\cot x$ and above values one can plot the graph of $\cot 4x$