Starting claim (at the left): 2 + |x - 3| > 4
Subtract 2 from both sides, to get:
|x - 3| > 2
Thus, x - 3 must NOT lie between -2 and +2, that is:
Either x - 3 < -2 or x - 3 > +2
Add +3 to all sides, to get:
x - 3 + 3 < -2 + 3 or x - 3 + 3 > +2 + 3

In other words: Either x < +1 or x > 5

Solution Set in interval notation: ( - , 1 ) ( 5, + )

Solution set pictured on a number line