We are given the inequality:

$|x - 6| \leq 10$

Step 1: Understand the Absolute Value Inequality

An absolute value inequality like $|x - 6| \leq 10$ means that the expression inside the absolute value, $x - 6$, is constrained to be between $-10$ and $10$. This is because the absolute value of a number represents its distance from 0, so the inequality $|x - 6| \leq 10$ can be rewritten as:

$-10 \leq x - 6 \leq 10$

Step 2: Solve for $x$

Now, to solve for $x$, we add 6 to all parts of the inequality:

$-10 + 6 \leq x - 6 + 6 \leq 10 + 6$

Simplifying the inequality:

$-4 \leq x \leq 16$

Step 3: Conclusion

The solution to the inequality is:

$-4 \leq x \leq 16$

Thus, the correct answer is Option B: $-4 \leq x \leq 16$.

Would you like any further details or explanations?

Here are five related questions to practice:

1. Solve $|x + 5| \leq 7$.
2. Solve $|x - 3| \geq 8$.
3. What does $|x - 2| < 4$ represent on a number line?
4. How would you solve $|x + 1| > 3$?
5. How does the solution change if we replace $\leq$ with $\geq$ in $|x - 6| \leq 10$?

Tip: For absolute value inequalities, remember that $|A| \leq B$ becomes $-B \leq A \leq B$, and $|A| \geq B$ becomes two separate cases $A \geq B$ or $A \leq -B$.