Two lines are parallel if the have the same slop. The slope can be seen if you write the equation of the line in the form
[tex]y=mx+b,[/tex]
in this case m is the slope. So, if you write the last equation, the one that is selected in this form, you have
[tex]\begin{gathered} 3x-2y=12 \\ 2y=3x-12 \\ y=\frac{3}{2}x-6 \end{gathered}[/tex]
so the slope is 3/2 and it is different from the original one. On the other hand, if we analyze the third equation
[tex]\begin{gathered} 3x+2y=-2 \\ 2y=-3x-2 \\ y=\frac{-3}{2}x-1 \end{gathered}[/tex]
we see that the slope of 3x+2y=-2 is the same that the slope of y=-3/2x-5, so they are parallel.
