Question 985144
You are trying to ask for the Additive Inverse Property.


Adding the OPPOSITE of a number is the same as SUBTRACTING the number.  You can restate your first expression {{{2y-2y}}} as  {{{2y+(-2y)}}}.  We have no inverse property for subtraction; we must understand subtraction both in the usual way, AND  as adding the opposite of a number.


Both the expressions you asked ARE equal to 0.
{{{2y-2y=0}}}
and
{{{-2y+2y=0}}}.