Again these measurements can not be true if you have a hexagon with a side of 6 the apothem is 3√3

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Two segments drawn from the center of a regular hexagon to adjacent vertices create an equilateral triangle.  The altitude of that triangle is the apothem of the hexagon.  Since an altitude of an equilateral triangle is also an angle bisector, the apothem creates two congruent 30-60-90 triangles from the original equilateral triangle.  In this problem, the apothem bisects the side of the hexagon (6cm).  Applying a property of 30-60-90 triangles, you are correct, the apothem of the base of the pyramid should be 3√3 cm, not 4cm.