Why might you want to use the Communative Property to change the order of the integers in the following sum before adding? For example: -80 + (-173) + (-20)

An operation follows the Commutative property if changing the order of the numbers in the operation does not change the outcome. Thus, addition (and multiplication) are commutative (i.e., a+b=b+a or a*b=b*a). 
In a problem where multiple numbers are being added together, you must remember that the Order of Operations dictates that you must work left to right. So in the case of
-80+(-173)+(-20)
The first two numbers are added together first, then the third number is added to that sum. Using the Commutative property to reorder the numbers can make the addition steps much easier, especially when doing mental math. This sum can be commuted as
-80+(-20)+(-173)
But now each addition step is easier. The first two numbers sum easily to -100, which is then an easy number to add to -173 (resulting in -273).
The Commutative property allows you to reorder things so that performing the operations may be simpler.