The colors that a person would need to mix in order to make royal blue are primary blue and purple. Since royal blue is a shade of blue, all you need to do is darken the blue to make royal blue.
The color wheel starts with three primary colors which are red, blue and yellow. These primary colors make three secondary colors which are orange, green and purple. Most colors come from mixing a primary color with a secondary color. Royal blue is a mixture of a primary blue and a secondary purple (blue and red mixed together in equal parts).