To determine how far a box will slide with a coefficient of kinetic friction of 0.23 after an initial push of 4.2 m/s, one can apply principles of physics, specifically energy methods or kinematics. The problem is similar to another example where a box with a coefficient of 0.20 slides after being pushed to an initial speed of 4.0 m/s, yielding a calculated distance of 4.1 meters. The weight of the box is not necessary for the calculation, as the frictional force can be determined from the coefficient alone. Participants in the discussion emphasize the importance of understanding the underlying equations, suggesting that basic calculus knowledge is beneficial. Ultimately, the conversation highlights the collaborative effort to solve the problem and clarify the methods involved.