The 4-state model of anthraquinone molecules ordering in a pin-wheel large-pore honeycomb phase on Cu(111) is proposed and solved by Monte Carlo simulation. The model is defined on a rescaled triangular lattice with the lattice constant a being equal to intermolecular distance in the honeycomb phase. The pin-wheel triangle formations are obtained taking into account the elongated shape of the molecules and anisotropic interactions for main two attractive short range (double and single dimeric) H-bond interactions. The long-range intermolecular interactions, corresponding to repulsive dipole-dipole forces, are assumed to be isotropic. Also, a very small (compared to short-range forces) isotropic attractive long-range interaction at the "characteristic" distance of a pore diameter is employed, and its effect carefully studied. This interaction is crucial for a formation of closed porous ordered systems, pin-wheel hexagons in particular. If each side of a pin-wheel hexagon is formed of n parallel molecules, the distance of this characteristic interaction is a√(3n(2)+1). The phase diagrams including different pin-wheel hexagon phases and a variety of other ordered structures are obtained. By changing the distance of characteristic interaction, different ordering routes into the experimental pin-wheel honeycomb phase are explored. The results obtained imply that classical explanation of the origin of the pin-wheel honeycomb phase in terms of some balance of attractive and repulsive forces cannot be totally discounted yet.