Let's solve for x in each equation
2x + 6 = 2
2x = 2- 6
2x = -4
x= -2
2x + 6 = 2 has -2 as a solution
2(x- 4 ) = 6x
2x -8 = 6x
-8 = 4x - 2x
-8 = 2x
-8 = 2x
-4 = x
-2 is not the solution
3x + 1/2 = 1/4 x + 6
3x - 1/4 x = 6 - 1/2
11/4 x = 11 /2
11x /4 = 11/2
x = 11/2 (4/11)
x =2
-2 is not a solution
7 - 3x = 5x + 11
7 - 11 = 5x + 3x
-4 = 8x
x= -1/2
-2 is not a solution
3x + 15 = 2x + 9
3x - 2x = 9 - 15
x = -6
The only equation with a solution of -2 is;
2x + 6 = 2