We begin by solving the absolute value inequality:

$|t - 4| \leq 2$

This inequality means that the expression inside the absolute value, $t - 4$, lies within 2 units of 0. To remove the absolute value, we rewrite the inequality as a compound inequality:

$-2 \leq t - 4 \leq 2$

Now, solve for $t$ by adding 4 to all three parts of the inequality:

$-2 + 4 \leq t - 4 + 4 \leq 2 + 4$

$2 \leq t \leq 6$

Thus, the solution is:

$2 \leq t \leq 6$

This is the compound inequality that describes the solution set.

Would you like more details on solving absolute value inequalities?

Here are 5 related questions to expand your understanding:

1. How would the solution change if the inequality was $|t - 4| \geq 2$?
2. What are the steps to solve an inequality with a negative absolute value, such as $|t - 4| \leq -2$?
3. How do you solve absolute value inequalities with a variable on both sides?
4. Can you solve $|2t - 1| \leq 3$? What does the compound inequality look like?
5. How do you graph the solution $2 \leq t \leq 6$ on a number line?

Tip: Always isolate the absolute value term before solving these inequalities.