Recall the definition of absolute value:
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
Then the equation
2 |x - 3| + 6 = 4
breaks down into two cases.
(1) If x - 3 ≥ 0, then |x - 3| = x - 3, and so
2 (x - 3) + 6 = 4
2 (x - 3) = -2
x - 3 = -1
x = 2
(2) If x - 3 < 0, then |x - 3| = -(x - 3), and so
-2 (x - 3) + 6 = 4
-2 (x - 3) = -2
x - 3 = 1
x = 4
