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Absolute value is a fundamental concept in mathematics that refers to the non-negative value of a number without regard to its sign. In simpler terms, it’s the distance of a number from zero on the number line. For example, the absolute value of both 5 and -5 is 5 because both are 5 units away from zero.

To denote the absolute value, we use vertical bars. So, the absolute value of -8 is written as \(|-8| = 8\). Absolute values are always equal to or greater than zero.

Understanding absolute value is important because it helps simplify and solve equations by focusing only on the distance a number represents, not its direction.

Subtraction involving negative numbers can seem tricky but is straightforward once you grasp the rules. When subtracting a negative number, you can think of it as adding the positive opposite of that number. For example, \(-3 - (-5)\) is the same as \(-3 + 5\). This is because subtracting a negative is akin to moving in the positive direction on the number line.

In our specific problem, we have to simplify \(-8 - 6\). This isn't subtracting a negative but dealing with the summation of two negative numbers. Add their absolute values (8 and 6) and keep the negative sign, resulting in \(-14\).

Understanding this concept can help in dealing with more complex mathematical operations and equations.

The distance from zero is a way to understand the absolute value better. It measures how far a number is from zero on a number line, regardless of the direction. For instance, the distance from zero for both -10 and 10 is 10 units.

When solving problems involving absolute values, always remember this perspective. For example, with \(-14\), the distance from zero is 14 units, so \(|-14| = 14\).

Visualizing numbers on the number line and considering their distance from zero aids in comprehending absolute values and ensures clearer, more accurate computations.