Solve |x-4| < 8: Absolute Value Inequality Analysis

To solve the inequality $|x - 4| < 8$, we will break it down into two separate inequalities.

• First, recognize that $|x - 4| < 8$ means the expression $x - 4$ can vary between -8 and 8 without violating the inequality constraint.
• This gives us two inequalities to solve: $-8 < x - 4$ and $x - 4 < 8$.

Let's solve each inequality:
1. For $-8 < x - 4$:
- Add 4 to both sides to isolate $x$:
$-8 + 4 < x \rightarrow -4 < x$ 2. For $x - 4 < 8$:
- Add 4 to both sides to isolate $x$:
$x < 8 + 4 \rightarrow x < 12$

By combining these results, we obtain the solution:
$-4 < x < 12$

Therefore, the range of $x$ that satisfies the inequality $|x - 4| < 8$ is $-4 < x < 12$.

Hence, the correct statement from the given choices is $\boxed{-4 < x < 12}$.