We are given the inequality:

$-6x - 4 \leq -4$

Step 1: Isolate $x$

First, add 4 to both sides to eliminate the constant term on the left-hand side:

$-6x - 4 + 4 \leq -4 + 4$

This simplifies to:

$-6x \leq 0$

Step 2: Solve for $x$

Now, divide both sides by $-6$. When dividing by a negative number, remember to reverse the inequality sign:

$x \geq 0$

Step 3: Analyze the options

We need to check which of the given values does not satisfy the inequality $x \geq 0$.

The option provided is $x = -4$.

Since $-4$ is less than 0, it does not satisfy the inequality $x \geq 0$.

Conclusion:

The value of $x$ that does not make the inequality true is: $\boxed{-4}$

Would you like further details or have any questions about this solution?

Here are 5 related questions to explore:

1. How do you solve inequalities involving division by a negative number?
2. What happens to the inequality sign when multiplying or dividing by a negative number?
3. How would you represent this inequality on a number line?
4. What is the difference between strict inequalities and inclusive inequalities?
5. Can you verify the solution by substituting values into the original inequality?

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