 The train has length lb and there will be some time delta tb between the events and in this time the train will travel a distance v delta tb as shown on the diagram. So then the delta xb, the separation between the two events is the length of the train in Bob's frame plus the distance the train moves in this time. Now we have two expressions for delta xb, so I've got this one here and we've also got the Lorentz transform expression and equating these two we get. Finally sticking these two equations into the Lorentz transformation for time and doing a little bit of algebra gives us the desired result. Bob measures some length contraction, La over gamma.