1) a-b=5, c=2
a = b + 5
a = b + 5
a = b + 5
ab = 6
(b + 5)b = 6
b^2 + 5b = 6
b^2 + 5b - 6 = 0
(b + 6)(b - 1) = 0
b = -6, 1
a = -1, 6
abc = {-162, 162}

2) a+b=4, c=7
a = 4 - b
ab = 6
(4 - b)b = 6
4b - b^2 = 6
b^2 - 4b + 6 = 0
No real solutions, no set can be found.

3) a=3, b-c=6
a = 3, b = c + 6
ab = 6
3(c + 6) = 6
3c + 18 = 6
3c = -12
c = -4
b = 2
abc = {324}

4) ab=6, bc=3
ab = 6
bc = 3
a = 6/b
c = 3/b
a = 6/c
6/c = 3/b
6b = 3c
2b = c
6/b * 2b = 6
12 = 6
No real solutions, no set can be found.