To solve the absolute value equation:

$|x - 4| = 8$

Step 1: Consider the definition of absolute value

The absolute value equation $|A| = B$ means that $A$ can be either $B$ or $-B$:

$x - 4 = 8 \quad \text{or} \quad x - 4 = -8$

Step 2: Solve for $x$

1. $x - 4 = 8$
   $x = 8 + 4 = 12$

2. $x - 4 = -8$
   $x = -8 + 4 = -4$

Final Answer:

$x = 12,-4$

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Related Questions:

1. Solve $|x + 5| = 3$.
2. Solve $|2x - 7| = 9$.
3. Solve $|x^2 - 4| = 5$.
4. Solve $|x - 2| + 3 = 7$.
5. Solve $|3x + 1| = |x - 5|$.

Tip:

When solving absolute value equations, always check if the solutions satisfy the original equation, especially if there are restrictions.