We need to solve the equation involving the absolute value:

$|2x - 4| - 8 = -2$

Step 1: Isolate the absolute value term

First, isolate the absolute value by adding 8 to both sides of the equation:

$|2x - 4| = -2 + 8$ $|2x - 4| = 6$

Step 2: Set up two cases

The absolute value equation $|A| = B$ can be written as two separate equations:

1. $2x - 4 = 6$
2. $2x - 4 = -6$

Step 3: Solve both cases

Case 1: $2x - 4 = 6$

Add 4 to both sides: $2x = 10$ Divide by 2: $x = 5$

Case 2: $2x - 4 = -6$

Add 4 to both sides: $2x = -2$ Divide by 2: $x = -1$

Step 4: Final answer

The solutions to the equation are: $x = 5, -1$

Would you like a detailed explanation of any particular step, or do you have further questions?

Here are 5 related questions for more practice:

1. Solve $|3x + 7| - 5 = 2$.
2. Solve $|x + 4| = 0$.
3. Solve $3|x - 1| = 9$.
4. Solve $|5x + 2| + 4 = 10$.
5. Solve $|x + 6| = 3x$.

Tip: When solving absolute value equations, always remember to set up two cases to capture all potential solutions.