We report full-dimensional accurate quantum dynamical calculations of the rotationally inelastic collision: para-H-2(nu(1)=0,j(1)=0)+para-H-2(nu(2)=0,j(2)=0)-->para-H-2(nu(1)=0,j(1)('))+para-H-2(nu(2)=0,j(2)(')), using a wave packet approach based on the Chebyshev polynomial expansion of Green's operator. The six-dimensional Hamiltonian within the coupled-states approximation is discretized in a mixed grid/basis representation and its action is computed in appropriate representations facilitated by a series of one-dimensional pseudo-spectral transformations. Both the parity and diatomic exchange symmetry are adapted. The S-matrix elements for the rotational transitions are obtained at all energies by the Fourier transform of Chebyshev correlation functions and used to compute transition probabilities, differential and integral cross sections, and state-resolved thermal rate constants. Results are compared for two recently proposed ab initio based potential energy surfaces and with previous quantum results.