Starting from exact eigenstates for a symmetric ring, we derive a low-energy effective generalized Anderson Hamiltonian which contains two spin doublets with opposite momenta and a singlet for the neutral molecule. For benzene, the singlet (doublets) represent the ground state of the neutral (singly charged) molecule. We calculate the non-equilibrium conductance through a benzene molecule, doped with one electron or a hole (i.e. in the Kondo regime), and connected to two conducting leads at different positions. We solve the problem using the Keldysh formalism and the non-crossing approximation. When the leads are connected in the para position (at 180°), the model is equivalent to the ordinary impurity Anderson model and its known properties are recovered. For other positions, there is a partial destructive interference in the co-tunneling processes involving the two doublets and, as a consequence, the Kondo temperature and the height and width of the central peak (for bias voltage V_b near zero) of the differential conductance G = dI/dV_b (where I is the current) are reduced. In addition, two peaks at finite V_b appear. We study the position of these peaks, the temperature dependence of G and the spectral densities. Our formalism can also be applied to carbon nanotube quantum dots with intervalley mixing.