With intarsia you don't carry the colors but work with the background color up to a train car and then drop it and start with the car color, on the other side of the car use a different ball of background color and work to the next car and have a ball of that color to work with, dropping and adding new colors as needed. When you work back you pick up and drop colors as needed. Watch the video.
I was doing a motif once that I thought I could strand the yarn across sections of my intarsia. I was not happy with the result. I should have struck to intarsia the whole way. For your train you would use a separate ball for each car and the backgound sections between. You could do the black with intarsia as well or go back and do it with duplicate stitch afterward. For the bigger sections of black I think I'd have my intarsia going and for little things like the "9" on the red car, I think I would opt to add it in later with duplicate stitch.
It isn't that hard once you get it sorted out and understand about how to "twist" the colors at the changes so you don't get holes. Oh, I might add that you will have gaps where you change colors at first but you fix those with the tails when you're done and it looks good.