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We report on our new analysis of the spatial and kinematic distribution of warm and cold molecular gas in the nearby, prototypical, luminous infrared galaxy NGC 6240, which was undertaken to explore the origin of its unusually luminous H₂emission. The gas components are known to be distributed between the two merging nuclei, forming an off-nuclear molecular gas concentration. By comparing three-dimensional emission-line data (in space and velocity) of CO J=2-1 in the radio and H₂in the near-infrared, we are able to search for the spatial and kinematic conditions under which efficient H₂emission is produced in much more detail than has previously been possible. In particular, we focus on the H₂-emitting efficiency, defined in terms of the intensity ratio of H₂to CO [I(H₂)/I(CO)], as a function of velocity. We derive this by utilizing the recent high-resolution, three-dimensional data presented by Tecza and coworkers. The integrated H₂-emitting efficiency is calculated by integrating the velocity profile of H₂-emitting efficiency in blue, red, and total (blue plus red) velocity regions of the profile. We find that (1) both the total H₂-emitting efficiency and the blue-to-red ratio of the efficiency are larger in regions surrounding the CO and H₂ intensity peaks, and (2) the H₂-emitting efficiency and the kinematic conditions in the warm molecular gas are closely related to each other. We compare two possible models that might explain these characteristics: a large-scale collision between the molecular gas concentration and the merging nuclei, and a collision between the molecular gas concentration and the external superwind outflow from the south nucleus. The latter model seems more plausible, since it can reproduce the enhanced emitting efficiency of blueshifted H₂around the molecular gas concentration if we assume that the superwind blows from the south nucleus toward us, hitting the entire gas concentration from behind. In this model, internal cloud-cloud collisions within the molecular gas concentration are enhanced by the interaction with the superwind outflow, and efficient and intense shock-excited H₂emission is expected as a result of the cloud-crushing mechanism. The observed spatial distribution of the H₂-emitting efficiency can be explained if there is a greater kinematic disturbance in the outer part of the molecular gas concentration, as a result of the interaction with the superwind outflow, and also more frequent cloud-cloud collisions in the region. In addition, the kinematic influence of the superwind on the molecular gas concentration should be larger at bluer velocities, and the collision frequency is expected to be larger at bluer velocities, explaining the relationship between velocity and the H₂-emitting efficiency.