I will guess that this means we are to find the maximum value of x+y, given the conditions and
The feasibility region is between the lines 7x+2y=-3 and 7x+2y=3; and between the lines y-x=-4 and y-x=4.
I'll let you do the ugly calculations to find the corners of the feasibility region; they are at (-11/9,25/9), (-5/9,31/9), (5/9,-31/9) and (11/9,-25/9).
Clearly the maximum value of x+y is at (-5/9,31/9); the maximum value is 26/9.
If your question was something completely different, resubmit it, in a format that is clearly understandable.