Answer
See graph and explanations.
Work Step by Step
Step 1. Given $g(x)=-2tan(x)$ and $h(x)=2x-\frac{\pi}{2}$, we have $y=(g\circ h)(x)=-2tan(2x-\frac{\pi}{2})$
Step 2. Start from $y=tan(x)$ (purple), we can obtain $y=tan(2x)$ (green) by shrinking horizontally with a factor of 2.
Step 3. Start from $y=tan(2x)$, shift the curve horizontally $\frac{\pi}{4}$ to the right, stretch vertically by a factor of 2 and then reflect around the x-axis to get the red curve for $y=(g\circ h)(x)=-2tan(2x-\frac{\pi}{2})$
