The given compound inequality is:

\[
-12 < 3 - 6 < 12
\]

We can solve it by breaking it into two parts:

### Part 1: Solve \(-12 < 3 - 6\)
1. Simplify the right side:
   \[
   -12 < 3 - 6 = -3
   \]
   So, the inequality becomes:
   \[
   -12 < -3
   \]
   This is true because \(-12\) is less than \(-3\).

### Part 2: Solve \(3 - 6 < 12\)
1. Simplify the left side:
   \[
   3 - 6 = -3
   \]
   So, the inequality becomes:
   \[
   -3 < 12
   \]
   This is also true because \(-3\) is less than \(12\).

Since both parts of the inequality are true, the solution to the compound inequality is valid. Therefore, the final answer is:

\[
-12 < 3 - 6 < 12
\]

Would you like more details on how compound inequalities work?

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Here are some related questions:

1. How do you solve compound inequalities with variables?
2. What happens if one part of the compound inequality is false?
3. Can compound inequalities involve absolute values?
4. How do you graph compound inequalities on a number line?
5. What is the difference between "and" and "or" in compound inequalities?

**Tip:** Always check each part of a compound inequality separately to ensure that both are true!

Understand how to solve the compound inequality -12 < 3 - 6 < 12 through simple step-by-step explanations. This solution covers core concepts like solving linear inequalities and using the transitive property, suitable for students in Grades 6-8.

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