To solve the inequality $|x - 2| - 4 > 2$, let's go through it step-by-step:

1. Isolate the absolute value: $|x - 2| > 6$

2. Rewrite the inequality without the absolute value: When solving $|x - 2| > 6$, we split it into two cases:

   • Case 1: $x - 2 > 6$ $x > 8$

   • Case 2: $x - 2 < -6$ $x < -4$

3. Combine the solutions: The solution to $|x - 2| - 4 > 2$ is: $x > 8 \quad \text{or} \quad x < -4$

So, the solution in interval notation is: $(-\infty, -4) \cup (8, \infty)$

Would you like more details on the steps? Here are some related questions:

1. How do you solve inequalities involving absolute values?
2. Can inequalities with absolute values ever have no solutions?
3. What happens when the inequality is $|x - 2| - 4 < 2$?
4. How can we graph this inequality on a number line?
5. How does solving inequalities differ from solving equations?

Tip: When solving absolute value inequalities, always remember to split the inequality into two cases for solutions.