The problem is asking for the solution set of the inequality involving absolute value:

$|2x + 4| < 8$

To solve this, we need to break the absolute value inequality into two parts:

Step 1: Remove the absolute value by setting up two inequalities:

$-8 < 2x + 4 < 8$

Step 2: Solve the compound inequality:

For the left inequality:

$-8 < 2x + 4$ Subtract 4 from both sides: $-12 < 2x$ Now, divide both sides by 2: $-6 < x$

For the right inequality:

$2x + 4 < 8$ Subtract 4 from both sides: $2x < 4$ Now, divide both sides by 2: $x < 2$

Step 3: Combine the results:

$-6 < x < 2$

So, the solution set is: $x \in (-6, 2)$

This is the set of all $x$ such that $x$ is greater than -6 and less than 2.

Would you like more details on this or have any questions?

Here are some related questions to expand on this concept:

1. How would you solve the inequality $|3x - 5| \leq 9$?
2. What happens if the inequality is $|2x + 4| > 8$?
3. How do you solve an absolute value equation like $|x - 7| = 10$?
4. What is the difference between solving $|x| < c$ and $|x| > c$?
5. How can absolute value inequalities be applied in real-world problems?

Tip: When solving absolute value inequalities, always remember to split them into two cases: one for the positive and one for the negative side.