Point M is equidistant from all vertices of a regular hexagon at a distance equal to 12

Point M is equidistant from all vertices of a regular hexagon at a distance equal to 12 and from its plane at a distance equal to 4. Find the length of the side of the hexagon.

If the internal angles are equal to 120 in the continuous hexagons, then if it is divided into 6 equal triangles they will be equilateral, which means the segment from the vertex to the center is equal to the side, and also equal to the caktet of a right-angled triangle with sides 4 and 12 and is equal to 8√2.