First of all, let's rearrange the second equation so that it comes in the slope-intercept form:
[tex]-2x + 8y = 6\iff x+4y=3 \iff y=-\dfrac{1}{4}x+\dfrac{3}{4}[/tex]
Now it becomes evident that the two lines have the same slope of -1/4. When two lines have the same slope, they are parallel.
