If the hexagons are regular, it has 3 quartets of parallel lines and one 6-tuple of parallel lines.
If the bases are irregular hexagons, it can have six pairs of parallel lines and one 6-truple.
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For a uniform hexagonal prism, there are four pairs of parallel sides. On a hexagonal prism, the six side faces have interior angles of 120 degrees, so each face is parallel with one three over from it. The ends (base and top) are parallel and 90 degrees from each side.
Four.
5 pairs of parallel lines, plus a set of 5 parallels.
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