x-y = 4     <--first equation

xy = 96     <--second equation

Solve the first equation for x

x = y+4

Substitute in the second equation:

(y+4)y = 96

y(y+4) = 96

y²+4y-96 = 0

(y+12)(y-8) = 0

y+12=0;  y-8=0
   y=-12   y=8

if y = -12, we substitute in

x = y+4      
x = -12+4
x = -8

So one answer is x = -8 and y = -12

if y = 8, we substitute in

x = y+4       
x = 8+4
x = 12

So the other answer is x = 12 and y = 8

Edwin