How to do equations with variables with the same coefficient on each side?

Example 1:

4x + 2 = 4x + 4 ... subtract 4x from both sides

4x - 4x + 2 = 4x - 4x + 4 ... simplify

2 = 4 (incorrect)

example 2:

4x + 2 = 4x + 2 ... subtract 4x from both sides

4x - 4x + 2 = 4x - 4x + 2 ... simplify

2 = 2 (correct)

* * if the variables cancel out ... and u r left with an incorrect statement (like in example 1), then ur equations will have no solution

* * if the variables cancel out ... and u r left with a correct statement (like in example 2), then ur equations will have infinite solutions