No. Hexagons and squares will each tessellate by themselves but one can not make a tessellation out of hexagons and squares combined.
However, if you add in a third shape, the triangle, one can make a tessellation.
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Triangle, square and hexagon
A regular hexagon will tessellate. Other hexagons may or may not tessellate.
Equilateral triangle, square and regular hexagon.
If it's a regular hexagon it will tessellate.
Yes.