Thanks for the advice of dividing and multpling of gamma. I also had a confusion, so I paused the video, First figured out why it got divided and then rememberd this N = YM (N-nomal, Y-gamma, M-moving) . When I resumed the playback, you just solved my problem. Coincidence!
And ship reached proxima in 3.19 years due to lorentz contraction.

At 3:47 . CTb = L/2 + VTb . The time in CTb refers to the total time light took to reach PofForward . And CTb represents Total Distance light took.
L/2 refers to the actual distance from candle to PofForward . But As the Distance increases due to moving train . Say it moved M feets away from the moment light was emmited . And when light reached PofForward, PofForward is now M feets away from the point where light only had to travel L/2 to reach PofForward (if train is at rest) .
So why light took Tb amount of time to cover that extra distance.? Isn’t Tb is meant to represent the total amount of time light took to reach PofForward ? If CTb and VTb are different , why amount of time (Tb) is same ?

you literally wrote textbooks on using microsot office apps?