A pair of parallel lines are the ones that never meet on the plane, they can never intersect regardless of how much we extend both lines.
So, using the definition above, we can notice that there is a line that intersects the other three lines. Therefore, that one cannot be parallel with any of the others three lines.
As for the remaining three lines, we see that each of those is parallel to any of the others, so, the three lines are parallel. However, we need to identify pairs of parallel lines, since we have 3 parallel lines, there are 3 different pairs that we can form with them (1,2), (2,3), (3,1).
Therefore, there are 3 pairs of parallel lines in the image.