If I understand your question correctly then you have a six sided pyramid (with a regular hexagonal base) with side lengths 2cm and corner to top-point length 6cm?

If so, a regular hexagon is made up of six regular (equilateral) triangles, so you know the distance from a corner to the centre of the hexagon is also 2cm. If you take a cross section of the pyramid across two opposite corners you will have a 2d triangle of which you know the length of the base and hypotenuse. You should be able to work out the height using standard trig from here