Answer
See graph and explanations.
Work Step by Step
Step 1. We can identify the given function $y=4\ tan(2x)$ has a period of $p=\frac{\pi}{2}$ and vertical asymptotes at $x=\pm\frac{\pi}{4}, \pm\frac{3\pi}{4}...$
Step 2. We can use the following transformations to graph the function: start from $y=tan(x)$, shrink the curve horizontally by a factor of 2 and then stretch vertically by a factor of 2 to get the red curve shown in the figure.
