The discussion revolves around calculating the astronaut's velocity after throwing a 10 kg oxygen tank at 12 m/s. Participants emphasize using the conservation of momentum principle, noting that the total momentum before the throw is zero, so it must remain zero afterward. The initial calculations suggest the astronaut's velocity is -1.9 m/s, indicating movement in the opposite direction, but there is confusion with another participant suggesting -9.1 m/s. The conversation highlights the importance of distinguishing between speed and velocity, as the question specifically asks for velocity. Ultimately, the correct interpretation of the problem leads to a consensus on the astronaut's backward velocity.