Can we start a wave $\sin(2x-4)$ from position 4 in the horizontal axis?
You can shift the origin to $x=a$ by replacing the argument $x$ by $x-a$:

$$\sin(2(x-a))\tag{1}$$

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. $(1)$

$$\sin(2(x-4))=\sin(2x-8)\tag{2}$$