Distance Between Numbers

How far apart are -2 and 6 on the number line? Count it: 2 steps from -2 up to zero, then 6 more to reach 6, so 8 steps. Subtraction finds it at once: $\left|-2-6\right|$ is $\left|-8\right|$, which is 8.

Why the absolute value bars? A difference can come out negative, depending on which number you take from which: $-2-6$ is -8, while $6 - \left(-2\right)$ is 8. A distance is never negative, so the bars keep only the size. That also means the order does not matter: $\left|6 - \left(-2\right)\right|$ is 8 as well.

So the distance between two numbers is the absolute value of their difference. As always with bars, work out what is inside them first, then drop the sign.