How to sketch $y=2\cos\,2x+3\sin\,2x$ , $x$ for $[-\pi,\pi]$. 
Use addition of ordinate to sketch the graph of  $y=2\cos\,2x+3\sin\,2x$  , $x$ for $[-\pi,\pi]$.

I know that there will be three line in graph from the example it show that
$x=0$, $x=\frac{\pi}{4}$, $x=\frac{\pi}{2}$ and something like that I haven't no clue how to do. Can you please explain in step by step, so that I'll be able to do other questions.
Answer look like this.
Thanks.!

You probably know the graph of $y=\cos(\theta)$ and of $y=\sin(\theta)$ on $[-2\pi,2\pi]$.
The graph of $y=\cos(2\theta)$ on $[-\pi,\pi]$ is obtained from the graph of $y=\cos(\theta)$ on $[-2\pi,2\pi]$ by performing a horizontal compression by a factor of $2$ (we are making the change from $y=f(x)$ to $y=f(2x)$). 
Likewise, the graph of $y=\sin(2\theta)$ on $[-\pi,\pi]$ is the result of compressing horizontally by a factor of 2 the graph of $y=\sin(\theta)$ on $[-2\pi,2\pi]$.
The graph of $y=2\cos(2\theta)$ is obtained from the graph of $y=\cos(2\theta)$ by performing a vertical stretch by a factor of $2$. The graph of $y=3\sin(2\theta)$ is obtained from the graph of $y=\sin(2\theta)$ by performing a vertical stretch by a factor of $3$.
Once you have the graphs of both $y=2\cos(2\theta)$ and $y=3\sin(2\theta)$ (obtained by the simple geometric operations described above) you obtain the graph of
$$y= 2\cos(2\theta) + 3\sin(2\theta)$$
by "addition of ordinate". You want to imagine that you are graphing $y=3\sin(2\theta)$ "on top of" the graph of $y=2\cos(2\theta)$, so that you end up adding the values. You can get a fairly reasonable geometric approximation by doing this.
