Final answer:
The numbers -21, |1-20|, 13, and |14| are ordered from least to greatest as -21, 19, 13, 14 taking into account that absolute values represent distance from zero on the number line.
Step-by-step explanation:
To order the given numbers from least to greatest, we must understand the value of each number and its position on the number line relative to others.
-21 is the smallest number as it is the furthest below zero.
The absolute value symbol, denoted by | |, means the distance from zero. So, |1-20| simplifies to |-19| which is 19. This is positive and less than 13.
Next is the absolute value of |14| which is simply 14, greater than 13.
Finally, 13 is the largest of the given integers that are not enclosed by absolute value symbols.
Therefore, the correct order from least to greatest is:
-21, |1-20|, 13, |14|