We report D-2-NMR measurements on a single crystal of superconducting alpha-(h(8)-BEDT-TTF)(2)ND4Hg(SCN)(4), where h(8)-BEDT-TTF is bis(ethylenedithiotetrathiafulvalene), C10S8H8. The temperature dependence of the spectrum has revealed that two phase transitions occur on cooling; first at T-A = 132 - 150 K, where a single resonance peak splits into two subpeaks, and second at T-B = 20 K, where the subpeaks disappear after the broadening at 25 K. The former associated by temperature hysterisis is a first-order phase transition and the splitting width follows (1-T/T-A)(1/2) dependence. This splitting, which is so sensitive to the field orientation due to I = 1, is found to be caused by the quadrupole interaction. The spin-lattice relaxation rate T-1(-1) is strongly elongated by three orders of magnitude with decreasing temperature from 200 K, followed by the maximum around 40 K. This dramatic effect is interpreted by the Bloembergen-Purcell-Pound model applied to the quadrupole interaction. Discussions are made from the viewpoint of the dynamics of noncentrosymmetric tetrahedral molecule ND4+; at T-A, the uniform rotation might switch to the thermally activated hopping motion between preferable sites bonded to nitrogens of (SCN)(-1) legands and then the order-disorder transition might eventually occur at T(B )to form an anion ordering.