It's best to start by getting your equation into slope intercept form y=mx+b, where m is the slope
Given -x+4y=20, solve for y
4y=x+20
y=(1/4)x+5
If two lines are parallel, they will have the same slope. If two lines are perpendicular, they will have opposite reciprocal slopes (2/3 and -3/2, for example).
Solving for y, the first equation is y=(1/4)x+2. This has the same slope as the given equation, so the two are parallel.
The second equation is y=-4x-1, with -4 being the opposite reciprocal of 1/4. These two are perpendicular.
The third equation has slope -1/4, which is opposite but not the reciprocal, so it falls into the neither category.
The final equation also has slope -4, again the opposite reciprocal of 1/4. This line is perpendicular.
