The inequality you are working with is:

$|2x + 4| + 4 \leq 6$

Let's solve this step-by-step:

Step 1: Simplify the inequality

First, subtract 4 from both sides to isolate the absolute value term:

$|2x + 4| \leq 2$

Step 2: Solve the absolute value inequality

An absolute value inequality of the form $|A| \leq B$ can be rewritten as:

$- B \leq A \leq B$

So, for your case:

$-2 \leq 2x + 4 \leq 2$

Step 3: Solve the compound inequality

Now, solve this compound inequality by first subtracting 4 from all parts:

$-2 - 4 \leq 2x \leq 2 - 4$

$-6 \leq 2x \leq -2$

Now, divide everything by 2 to solve for $x$:

$-3 \leq x \leq -1$

Step 4: Write the solution in interval notation

The solution to the inequality is:

$[-3, -1]$

Step 5: Graph the solution

On the number line, you would mark a solid dot at $x = -3$ and another solid dot at $x = -1$, with a line connecting them. This indicates that all the values between and including -3 and -1 are part of the solution.

Would you like to know more about any of the steps, or have additional questions?

Related Questions:

1. What is the process for solving an absolute value inequality when it has a "greater than" sign instead of "less than"?
2. How would the solution change if the inequality was $|2x + 4| + 4 > 6$?
3. How do you graph strict inequalities on a number line?
4. What are the properties of absolute value that help simplify these types of inequalities?
5. Could this inequality have been solved using another method, like testing points?

Tip: Always double-check your solution by plugging in values from the interval back into the original inequality to ensure correctness.