What is parallel to 6x - 2y = -7 perpendicular to 6x - 2y = -7
-2x + 6y = 2
3x - y = 5
8x - 2y = 7
9x - 3y = 8
x + 3y = 12
and what is neither

Rearrange all of them in terms of y:
6x - 2y = -7
y = (-6x -7)/-2
y = 3x + 7/2

1) - 2x + 6y = 2
y = 1/3x + 1/3

2) 3x - y = 5
y = 3x - 5

3) 8x - 2y = 7
y = 4x - 7/4

4) 9x - 3y = 8
y = 3x - 8/3

5) x + 3y = 12
y = -x/3 + 4

Parallel lines have equal gradients; the gradient is the coefficient of x.
2 and 4 are parallel to the original eq'n as they have 3x just like the original eq'n.

Perpendicular lines have gradients that are negative reciprocals of each other; they multiply to give -1.
5 is the only one perpendicular to the original as -x/3 * 3 = -1

1 and 3 are therefore neither.