If we have an inequality |y| > 3, this will be satisfied if => y > 3 or y < -3.
So, the above inequality simplifies to two inequalities
Inequality I: |x - 3| - 4 > 3
|x - 3| - 4 > 3 => |x - 3| > 7
x - 3 > 7 or x - 3 < -7
Or, x > 10 or x < -4
Of, x lies outside of -4 and 10. Or, x can lie in the range (-∞, -4) or ( 10, ∞)
Inequality II: |x - 3| - 4 < -3
|x - 3| - 4 < - 3
=> |x - 3| < 1
=> -1 < x - 3 < 1 or x lies between 2 and 4
So, final solution is given by the range
( -∞, -4) or (2, 4) or ( 10, ∞)