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There cannot be a 3-d shape all of whose faces are regular hexagons.

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that claim above is not true, because for example a classic soccerball consists of hexagons.

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Q: How many faces would a 3D shape have whose faces were hexagons?
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What is a polyhedron that is a prism with two bases that are hexagons and the other faces are rectangles?

It's called, not altogether surprisingly, a hexagonal prism. If the bases were hexagons and the other faces were triangles, it would be a hexagonal antiprism.


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What solid shape has 4 less faces than a cube?

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