Question

determine 2 integers whose sum is 6 and difference is -6

Answer 1

0 and 6.

0+6 = 6
0-6  = -6 

Answer 2

Let the two integers = x and y

Sum=6
x+y=6 (1)

Difference =-6
x-y=-6 (2)

Solving (1) and (2),
We get x=0

Substitute x=0 in (1)
x+y=6
o+y=6
y=6

So the two integers are 0 and 6.