Question 937050
Best is just to solve each equation, and then check the possibilities for |x+y|.


{{{abs(x+3)=2}}}
either {{{-x-3=2}}}
{{{x+3=-2}}}
{{{x=-5}}}
or {{{x+3=2}}}
{{{x=-1}}}


{{{abs(y+1)=6}}}
either {{{-y-1=6}}}
{{{y+1=-6}}}
{{{y=-7}}}
or {{{y+1=6}}}
{{{y=5}}}


Up to now you know x is -5 or -1
and 
y is -7 or 5


There are FOUR possibilities for {{{abs(x+y)}}}.
Which of them is in your list?


Try to follow my plan shown above.  
(solution process result adjusted)