A complete analytical model for the rotational and translational diffusion of molecules with a six-fold point symmetry on a hexagonal lattice is presented. It can be applied, in particular, to the diffusion of benzene molecules adsorbed flat on the basal plane of graphite in the case of incoherent scattering. Under the weak hindered approximation, the classical mechanics framework and making use of the van Hove formalism of correlation functions, the intermediate scattering function and its Fourier transform, the scattering law, are both obtained. They can be expressed as sums of exponential decays or Lorentzian functions, respectively, containing the contribution of each of the dynamical processes taking place. In the case of benzene lying flat on the substrate we expect translational diffusion, continuous rotations of isolated molecules and hindered rotations of molecules within clusters. Each particular diffusive mechanism can be recognized owing to its particular signature in the dependence of the quasi-elastic broadening on the momentum transfer.