To solve the inequality $|x - 4| \leq 2$:

1. Understand the inequality: The absolute value inequality $|x - 4| \leq 2$ means that the expression $x - 4$ is within 2 units of 0.

2. Remove the absolute value: This can be rewritten as two separate inequalities: $-2 \leq x - 4 \leq 2$

3. Solve the compound inequality:

   • First, solve $-2 \leq x - 4$: $-2 \leq x - 4$ Add 4 to both sides: $2 \leq x$
   • Next, solve $x - 4 \leq 2$: $x - 4 \leq 2$ Add 4 to both sides: $x \leq 6$

4. Combine the solutions: The solution to the inequality $|x - 4| \leq 2$ is: $2 \leq x \leq 6$

So, the solution to the inequality $|x - 4| \leq 2$ is $2 \leq x \leq 6$.

Would you like any details or have any questions?

Here are some related questions to expand your understanding:

1. How do you solve an absolute value inequality where the inequality symbol is $>$ instead of $\leq$?
2. What is the geometric interpretation of the solution to $|x - 4| \leq 2$?
3. Can you solve the inequality $|2x + 3| < 5$ using a similar method?
4. How does the solution change if the inequality is $|x - 4| \geq 2$?
5. What is the effect of adding a constant to the variable inside the absolute value on the solution set?

Tip: When solving absolute value inequalities, remember that the absolute value $|A| \leq B$ implies $-B \leq A \leq B$, and $|A| \geq B$ implies $A \leq -B$ or $A \geq B$.