To start, solve each equation for y.
1st equation) 3x+y=-2, subtract 3x, y=-3x-2
2nd equation) 2y-6x=4, add 6x, 2y=6x+4, divide by 2, y=3x+2
3rd equation) 2y=-6x-8, divide by 2, y=-3x-4
Now, for lines to be parallel, their slope must be the same. Using the equation y=mx+b where m is slope, you can determine the slope of each line.
1st line) y=-3x-2, slope of -3
2nd line) y=3x+2, slope of 3
3rd line) y=-3x-4, slope of -3
Comparing these lines, you can see that only lines 1 and 3 have the same slope, making those your parallel lines.