To solve the inequality $|3x - 6| < 12$, we can break it down into two separate inequalities:

Step 1: Break the absolute value inequality into two cases

1. $3x - 6 < 12$
2. $3x - 6 > -12$

Step 2: Solve each inequality separately

Case 1: $3x - 6 < 12$

$3x < 12 + 6$

$3x < 18$

$x < \frac{18}{3}$

$x < 6$

Case 2: $3x - 6 > -12$

$3x > -12 + 6$

$3x > -6$

$x > \frac{-6}{3}$

$x > -2$

Step 3: Combine the solutions

The solution to the inequality $|3x - 6| < 12$ is:

$-2 < x < 6$

This means $x$ must be greater than $-2$ and less than $6$.

Would you like further details on how to solve inequalities, or do you have any questions?

Here are some related questions:

1. How do you solve absolute value inequalities that involve "greater than"?
2. What are the steps to graphing the solution set on a number line?
3. How do you solve compound inequalities?
4. What happens if the inequality symbol is "greater than or equal to"?
5. How do you interpret inequalities involving absolute values in real-world contexts?

Tip: Always remember that when solving absolute value inequalities, you need to consider both the positive and negative cases separately.