Plan: We know that the full hexagon has exactly 24 equal triangles in it, so we will divide it by 6 (because it said to cut it into six pieces) to get 4. So we know that whenever we cut it into 6 equal pieces, each equal piece will contain 4 triangles.

Do: First we worked out all the combinations of 4 combined triangles, without the triangles touching each other diagonally. E.g:

That is because if we cut like that the triangles would come apart. In the end we had three combinations.

Check: We checked by cutting 3 hexagons, each with a different combination. If they all worked that means we were right. And this is how the pieces fit together.