Even though the wave of $\sin(2x-4)$ looks like this and it starts from position 2 out of curiosity I would like to know whether we could start it from position 4 like the wave of $\sin(2x)$ shown here.
You can shift the origin to $x=a$ by replacing the argument $x$ by $x-a$:
Since for $\sin(2x-4)=\sin(2(x-2))$ you have $a=2$, the origin is shifted to $x=2$. If you want to shift it to $x=4$, you get from Eq. $(1)$
I am not sure whether I understand the question completely.
First of all do you mean this?
Here ONE zero crossing of the sin-wave is at the point (4,0).
In general the sinus is has no real starting point since its periodic, therefor you get an infinite amount of zero-crossings.
Then you might want to look at the equation this way:
Here Phase represents the shift to the left.
In your case with the nested frequency and phase it looks like this:
$$sin(2*(x-2))$$ or $$sin(2*(x-4))$$