You have the following equations:
2x + 2 = 8
2x = 6
The previous equations are the same equation because you can subtract 2 both sides of the first equation, and in such a way you obtain the second equation. In fat, you have:
2x + 2 = 8 subtract 2 both sides
2x = 8 - 2
2x = 6
which is exactly the same second equation. This situation is enough to prove that both equations are equal and then have the same siolutions.