In high school, I had the same confusion. Personally, it is ok to regard -2x as a whole, but correspondingly, the coordinate axis X should be changed to the coordinate axis corresponding to -2x!

For example, the point where sin(-2x) is zero is -2x= 1/2*pi*n, pi is pi, and n is an integer.

And the corresponding x is-1/4 * pi * n, of course, the negative sign here can be omitted according to the situation.

We can think that the sin function is still the same function, except that we have enlarged the points on the X axis and the direction is reversed.

We can also think that the coordinate axis is unchanged, but we have shrunk the sin function along the X axis, and the direction is reversed.

Of course, the second idea is recommended in the high school tutorial. Even if the coordinate axis is still x and y, we should make the function bigger, smaller, left, right and so on.

In the field of calculus, or the problem of space vector rotation, sometimes it is more convenient to change the coordinate axis.