A red light flashes at position xR = 3

An event that happens at time t and position x in S happens at time t' and position x' in S' where:

x' = gamma [x-vt] (1)

t' = gamma [t-vx/c^2] (2)

where

gamma = 1/sqrt[1-v^2/c^2]

Here it is assumed that at time t = 0, the origins of the coordinate systems S and S' coincide and that the clocks of both systems are set equal.

Using (2) you can relate the time difference of two events in S' to the difference in position and time of the events in S:

delta t' = gamma [delta t - v/c^2 delta x]

If delta t' = 0, then:

v = c^2 delta t/delta x

If you insert in here the time differences and spatial distances between the two light flashes, you find:

v = 0.899 c =2.696*10^8 m/s

gamma = 2.2874

and the events in S' have the coordinates:

x_{R}' = gamma [x_{R} - vt_{R}] = -11.64 m

t_{R}' = gamma [t_{R} - v/c^2 x_{R}] = 4.804*10^(-8)s

x_{B}' = gamma [x_{B} - vt_{B}] = -9.017 m

t_{B}' = gamma [t_{B} - v/c^2 x_{B}] = 4.804*10^(-8)s