keep on the right side
keep on the right(-hand) side
To remain on the right-most side (of something, especially a road or path). Turn right and walk toward the Main Street Bank, keeping on the right-hand side of the road as you go, and you'll be sure to see our shop. I always have to remind myself to keep on the right side of the road when I drive in America.
keep on the right(-hand) side (of something)
to stay on the right-hand side of something. We always keep on the right side of the road in this country. Please keep on the right-hand side.