This is the well-known zöllner illusion, named after johann zöllner who first drew the optical illusion in 1860. which method would allow you to prove that all seven long diagonal lines are parallel?

IF the lines are parallel, then any place one of them meets a horizontal side of the big square, it'll make the same angle with the side, and any place one of them meets a vertical side of the big square, it'll make the same angle with the side.  You could compare the angles along a horizontal edge, and compare the angles along a vertical edge, and draw some conclusions from those comparisons.  That's the first choice listed, and it's valid.

You could also draw one big diagonal of the big square, from the upper left corner to the lower right corner ... or really any single line that crosses all seven of the lines that are already there.  Your new long line is a transversal that cuts all seven lines in question, so if any are parallel, they'll form equal alternate interior angles with it.  These angles don't necessarily have to be 45°, but they do have to be equal if a pair of the lines are parallel.  You can compare a bunch of angles and spot whether any of the seven lines are parallel to any others.  That's the third choice listed, and it's valid.

The second choice is no good, because you don't know whether the tick marks are evenly spaced, and even if they are, equal numbers of tick marks only tell you about the length of the lines, nothing about whether they're parallel or not.

The last choice says "clearly".  What that's actually saying is "LOOK at these with your eyes and your brain and decide whether or not they're parallel." 

Two things about this choice:

#1).  NEVER trust your eyes or your other senses to make conclusions
about measurements.  If you do that, you'll convince yourself that the
Earth is flat, that everything in the sky goes around the Earth, that the
sun and the moon are both the same size, that airplanes and trucks
get smaller as they get farther away from you, and that NASA is lying
to all of us.  The result of THAT will be that anybody with a good half
of his brain will smile when he meets you, and secretly regard you as
a nutcake. 

#2).  This drawing is called the "Zöllner Illusion".  An "illusion" is something
that is not what it looks like.  Reasonable, intelligent people have been calling
this drawing one of those for the past 156 years ... since Zöllner first drew it ! 
That should begin to make you suspicious, and warn you NOT to rely on what
your eyes and brain are telling you, but to check it out.