Using the matrix method for ratios: We are given blue:red is 2:1 and red:orange is 6:1

Blue----------------------Red----------------------Orange
2--------------------------1 -------------------------0
0--------------------------6--------------------------1

We need the ratios to 'align' and the only way to do this is to multiple the first row by 6 so that the red aligns with the orange's '6' as such:

Blue----------------------Red----------------------Orange
12-------------------------6--------------------------0
0--------------------------6--------------------------1

Now that we have the alignment, the final ratio is as such: Blue:red:orange = 12:6:1
The total is therefore 12+6+1 = 19 and 38 is the only multiple of 19 so the answer is A.

Please excuse my terminology (alignment, matrix method...) I'm not sure what the actual method is called but it surely works.

We're given 2 ratios,

Blue:Red = 2:1
Red:Orange = 6:1

Let's balance these so we can compare them to each other.
Blue:Red = 12:1 (by multiplying the ratio with 6)
So the ratio of all three colours is,

Blue:Red:Orange = 12:6:1

Lets assume these are the actual number of cars, we get the sum to be 19. Since 19 is not an option, we want a multiple of 19, only 38 fits. Therefore we choose A.

blue : red = 2 : 1 = 12 : 6
red : orange = 6 : 1

So, blue : red : orange = 12 : 6 : 1
total = 12 + 6 + 1 = 19

total cars would be 19 or multiples of 19.

Ans: A