Okay, look at it this way. Imagine a train that is 300,000 km long and there are clocks located at the front and rear. They have been synchronized.
Now the train whips by the train station at 260,000 km per second.
Those at the train station will notice that the clock at the rear of the train is ahead of the clock at the front by 0.866 of a second, and they will see that the length of the train at this speed has shrunk down to 150,000 km, and they also will notice that the clocks on board the train are ticking at half speed.
Those on board the train still think that the two clocks are still synchronized, and they still think that the spatial length of the train is 300,000 km long.
And so if a burst of light is sent from the rear to the front of the train, the observers at the train station will see that it takes about 3.73 seconds for the light to reach the front of the train.
This is because the light is only going roughly 40,000 km per second faster than the train. Thus 150,000 km divided by 40,000 km per second, equals 3.73 seconds.
But for those on board the train, 3.73 seconds becomes 1.866 seconds since their clocks are ticking at half speed. But due to the clock offset of 0.866, they will measure 1.866 - 0.866 which equals 1.000 second. Now since they still think that the spatial length of the train is still 300,000 km, they think that the light had crossed 300,000 km in one second, hence the speed of light.