###Translate
ClearAll[triHex];
triHex[w_, h_] := Module[{hex = {FaceForm[White], EdgeForm[Black], Polygon@#,
Red, PointSize[Large], Point@#} &@ Table[{Cos[2 Pi k /6], Sin[2 Pi k /6]}, {k, 6}]},
Fold[Translate[#, {{0, 0}, ## & @@ #2}] &, hex,
{Table[{4 k Cos[Pi/3], 0}, {k, 1, w }], Table[2 k {Cos[Pi/3], Sin[Pi/3]}, {k, 1, h }]}]]
Examples:
Graphics[triHex[10, 5], ImageSize -> 600]
Graphics[triHex[7, 7] /. White -> LightBlue, ImageSize -> 600]
