A time-dependent wave packet method has been developed to study atom-triatom ABC+D-->AB+CD reactions in full six dimensions (6D). The approach employs a body-fixed coupled angular momentum basis for three angular coordinates, and three 1D bases for three radial coordinates. It permits the calculation of diatom AB vibrational state resolved total reaction probability for an initial rovibrational state of the triatom ABC. The approach is applied to study the H+H2O-->H-2+OH reaction on the modified Schatz-Elgersman potential energy surface. Initial state-selected total reaction probabilities are presented for initial ground and several vibrationally excited states of H2O for total angular momentum J=0, along with the final OH vibrational state distributions. We also report the cross sections for reaction from the initial ground vibrational and the first bending excited states of H2O. Comparisons are made between our results and those from other theoretical calculations and experiments.