Infinite number of shapes: there is no limit. Not all have sides in the usual sense: e.g., you could say a circle (or an ellipse or a kidney-shape) has one and a crescent has two, but they're curvesd, not straight.
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Try counting the sides.
An hexagon has 6 sides
5 Shapes, 8 sides
polygon
Infinitely many. Every regular polygon with 2n sides has n pairs of parallel sides. Then there are irregular polygons which can have parallel sides. And there are also irregular shapes which have parallel sides.