In a regular hexagon, each side is contained in a separate equilateral triangle with side of 2-units. That makes six equilateral triangles with side 2-units.
Further, each equilateral triangle of side 2-units contains four (4) equilateral triangles of side 1-unit.
Therefore the total number of equilateral triangles of side 1 units in a hexagon with side two units is 6*4=24.