Deuteron NMR relaxation and spectra were studied at the resonance frequency of 46 MHz in polycrystalline (ND(4))(2)PtCl(6) between 300-5 K. The relaxation rate maximum near 50 K is about 53% smaller than the calculated maximum related to 120 degrees rotations about the threefold symmetry axes of the ammonium ion. The difference is explained by assuming for a N-D vector a total of 24 equilibrium directions, which in groups of six deviate from the nearest Pt-N vector by a certain angle Theta. So-called limited jumps between the directions of each group take place much more frequently than the large-angle rotations, thus rendering a fraction of the deuteron quadrupole coupling ineffective in relaxation. A motional model is presented, which takes into account both these motions simultaneously. A comparison with experimental data leads to Theta=26.0 degrees , in reasonable agreement with earlier neutron diffraction data. A sharp decrease found in the relaxation rate at the order-disorder phase transition temperature of 27.2 K is related to the fact that one of the six equilibrium directions becomes preferred. This leads to a formation of ordered domains, in which the active motion driving the relaxation is 120 degrees rotations. Two components in the spectra found below 55 K are related to domains (broad) and transition regions between domains (narrow). Reasons for the nonexponentiality observed below 20 K are discussed, the most likely explanation being that limited jumps dominate within transition regions and make the corresponding deuterons relax faster than those in domains.