since x can be postive or negative

solve for both

x is positive

x - 3 + x + 3 = 6

2x = 6

x = 3

x is negative

-x - 3 - x + 3 = 6

-2x = 6

x = -3

so your solution set is [-3,3]

to test this let x = a number within this set like 2

|2 - 3| + |2 + 3| = 6

if you graph this you will see a horz line between (-3,6) to (3,6)