start with the math or the geometry.
you immediately see 3 or 4 useful ideas that might help:
3 series of lines will make such a grid. One sloped up, one down, and one flat.
a equilateral hexagon is made of 6 such triangles
the hexagon with 2 more triangles is a simple rhombus with 2 opposite 120 degree angles and 2 opposite 60 degree angles.
so you can cookie-cutter place any of {hexes, rhombi, or triangles} to make such a grid or you can draw a bunch of lines. The lines is the easy way. But any of it will work.
a slightly more advanced graphics approach can twist a pile of boxes into it.