We can draw the following to give us some idea of the situation
When we are told that we are going to reflect this point over x=1, we must notice that the point (-2,3) is on the left side of the line x=1. Then, the question translate to finding a point (x,y) that is on the right side of x=1 and that is at the same distance from the line x=1 as the point (-2,3).
To find this point, we are going to draw a horizontal line that passes through the point (-2,3). Then, starting at point (-2,3) we are going to "walk" along the line, until we cross the line x=1. When we do so, we calculate the distance between the point (-2,3) and the line x=1. Finally, with this distance, we "walk" the same distance on the line to find the point we wanted.
In a drawing, this process would look as follows
So far, with this picture we can see that the distance from (-2,3) to x=1 is 3. So the distance from x=1 to the desired point is should also be 3. Since (-2,3) and the desired point are on the horizontal (red) line, the must have the same y coordinate. That is, 3. So, we can see that the distance from (-2,3) to x=1 can be calculated by simply subtracting 1 and -2. That is (1-(-2)) =3.
Let h be the x-coordinate of the desired point, so it must happen that
Then, if we add 1 on both sides, we get
So the final result is the point (4,3)