Answer
$Period = \frac{\pi}{3} $
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 $y = 2 \tan 3 x$
$Period = \frac{\pi}{3} $
Some values
$y = 0, at\ x = 0, \frac{\pi}{3}$
$y = 2\ at\ x = \frac{\pi}{12}$
$y = -2\ at\ x = \frac{\pi}{4}$
$y -> \pm \infty\ at\ x =\frac{\pi}{6}$
Using graph of $\tan x$ and above values one can plot the graph of $2 \tan 3 x$
