One way is to image that you are observing things from somewhere nearby to the speeding rocket (but is stationary with respect to the Earth.)
Suppose the spaceship flies past you from left to right. The astronauts will, hopefully, have synchronised their two clocks with each other - but they would be synchronised only in reference frames that are stationary with respect to the spaceship. Relativity tells us that the clocks would not appear to us to be synchronised – the leftmost (rear) clock would appear to be running ahead of the forward clock. However, the astronauts see nothing of the sort – to them, the clocks still appear to be synchronised.
(Another thing we’d notice is that the spaceship would appear very foreshortened. Because of this length contraction, to us, the light would take even less time to get from the front clock to the back clock. Again, the astronauts notice nothing unusual about the length of their ship.)
When the two (now stopped) clocks are compared with each other they will show a bigger difference in time than would have been the case had this relativistic asynchronisation not been happening.
In other words, the asynchronisation is of the just the right amount to make sure that the readings on the clocks tell the astronauts that the light took exactly the expected amount of time to get from front to back, giving a velocity of c. The amount of asynchronisation compensates precisely for both the rocket’s velocity toward the light source and its length contraction (as observed by us).
