The given inequality to solve is:

$-3 |x| > -6$

Step 1: Divide both sides by $-3$ to eliminate the negative coefficient.

Dividing by a negative number reverses the inequality sign:

$|x| < 2$

Step 2: Interpret the absolute value inequality.

The inequality $|x| < 2$ means that $x$ lies between $-2$ and $2$. In other words, the solution is:

$-2 < x < 2$

Final Answer:

The correct solution is the interval:

$(-2, 2)$

This matches the first option in the choices provided.

Would you like further details or have any other questions?

Here are 5 related questions:

1. How do you solve inequalities involving absolute values?
2. What happens when dividing both sides of an inequality by a negative number?
3. Can you explain how to graph the solution $(-2, 2)$ on a number line?
4. How would the solution change if the inequality was $|x| \geq 2$?
5. What if the original inequality had a different coefficient for $|x|$?

Tip: Always remember to reverse the inequality when multiplying or dividing by a negative number!