1. **State the problem:** Evaluate the expression $$|5 - 10| - |-6| - 4$$. 2. **Recall the definition of absolute value:** The absolute value of a number $x$, denoted $|x|$, is the distance of $x$ from zero on the number line, which is always non-negative. So, $|a| = a$ if $a \geq 0$, and $|a| = -a$ if $a < 0$. 3. **Calculate each absolute value:** - Calculate $|5 - 10|$: $$5 - 10 = -5$$ $$|5 - 10| = |-5| = 5$$ - Calculate $|-6|$: $$|-6| = 6$$ 4. **Substitute these values back into the expression:** $$|5 - 10| - |-6| - 4 = 5 - 6 - 4$$ 5. **Simplify the expression step-by-step:** $$5 - 6 - 4 = (5 - 6) - 4 = -1 - 4 = -5$$ **Final answer:** $$-5$$