How many types of hexagons are there?

There is only one "hexagon" : it's a polygon with six sides. Now if you mean Polygons, there are infinite. starting with the triangle and then a new one every time you add a side to the current shape. (ex: triangle + one side = square; square + one side = pentagon; and so on...). All of this to the point were you cannot count/see the sides because they're too many and small and you get a Circle.