Primitive unit cell is such that contains lattice points only on unit cell vertexes. Non-primitive unit cell can contain lattice points also elsewhere, for example centered on unit cell face, on the middle of unit cell edges, un-centered ones inside face, etc. So basically hexagon cell can be both primitive and non-prmitive cell, depending on the chosen lattice structure, like pictured here :
Thus in general one can choose many configurations of cells representing some lattice.