Final answer:
A number line from -4 to 4 demonstrates that the absolute values of 4 and -4 are equal to 4 because the distance from zero to each point is the same, reflecting that absolute value measures magnitude without sign.
Step-by-step explanation:
The student's question involves understanding the concept of absolute value and how it reflects the distance from zero on a number line. To illustrate this, a number line is constructed from -4 to 4 with equal spacing between the tick marks. By using a ruler to measure the distance from 0 to 4 and from 0 to -4, one can observe that both distances are the same, indicating that the absolute values of 4 and -4 are both equal to 4. This is because the absolute value measures the magnitude of a number without considering its sign, which corresponds to the non-directional concept of distance. The concept of displacement mentioned in the reference texts gives an insight into understanding that the magnitude of a number (displacement) is always positive, similar to the idea of distance in physical space.