Louis ran to versailles and then walked back to town. his running rate was 6 kph and his walking time rate was 3 kph. how far was it to versailles if the trip took 6 hours?

Givens
Running rate = 6 km / hr
Walking rate = 3  km / hr

Let the running time = T
Let the walking time = 6 - T

Formula 
d = r * t

Sub and Solve
The distance going there is the same as the distance coming back. The times and rates are different, but the distance is the same. Therefore the two equations for distance are equal to each other.

6 * T  =  3 * (6 - T)  Remove the brackets on the right.
6T = 18 - 3T           Add 3T to both sides.
9T = 18                  Divide by 9
T = 18/9
T = 2 hours. 

Therefore it took him 2 hours to Run to Versailles.
The distance is 6*T = 6*2 = 12 km 
Answer = 12 km <<<<<<

It’s hard to understand what you put.. can you show a picture ?