1. **State the problem:** Solve the absolute value inequality $$6|x - 8| \leq 12$$ and find the values of $x$ that satisfy it. 2. **Recall the rule for absolute value inequalities:** For $|A| \leq B$ where $B \geq 0$, the inequality is equivalent to $$-B \leq A \leq B$$ 3. **Apply the rule:** Here, $A = x - 8$ and $B = \frac{12}{6} = 2$ (dividing both sides by 6 to isolate the absolute value). So, $$|x - 8| \leq 2 \implies -2 \leq x - 8 \leq 2$$ 4. **Solve the compound inequality:** Add 8 to all parts: $$-2 + 8 \leq x - 8 + 8 \leq 2 + 8$$ which simplifies to $$6 \leq x \leq 10$$ 5. **Write the solution in interval notation:** $x$ is between 6 and 10 inclusive. 6. **Answer the inequalities:** $$x \geq 6$$ $$x \leq 10$$