Yes: three sets of four.
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Three sets of four each.
Yes, a cuboid does have parallel edges. In a cuboid, all pairs of opposite edges are parallel to each other. Additionally, the opposite faces of a cuboid are also parallel to each other.
4 parallel edges
A cuboid has 6 faces, and each face has a pair of parallel faces. So, a cuboid has 3 pairs of parallel faces. Mathematically speaking, that's the tea, honey.