It's honestly difficult to understand what you are asking. Based on what you were saying in the other thread, I'm guessing that you are trying to say that the light beam will look like it's traveling at a different speed in a frame that is moving relative to the car than in the frame of the car itself. That's not the case. The speed of light is the same in both frames. The consequence of this is that the light beam is seen to hit the far side of the cart at different times in each frame. In the frame where the light beam has to travel further, it takes longer to traverse the distance and thus will take longer to reach its target. That's relativity of simultaneity.