The $^1H$ NMR spin-lattice relaxation in a series of the organic-inorganic hybrid systems $(C_nH_{2n+1}NH_3)_2SnCl_6$ (n = 8, 10, 12, 14) undergoing two successive phase transitions was studied. A discontinuity characteristic of a first order phase transition was observed at the high-temperature conformational transition. Besides, the spin-lattice relaxation rate below the conformational transition temperature was well fitted by four types of molecular motions, from which the chain-length dependence of the activation energies of the molecular groups was obtained.