Red is a primary color and cannot be produced by mixing other colors. Red, blue and yellow are the three primary colors. Only secondary and tertiary colors can be fabricated by mixing the appropriate colors together. Every color that exists originates from the primary colors.
Secondary colors are the result of two primary colors mixed together. Red and blue creates purple. Red and yellow creates orange. Yellow and blue creates green. The secondary colors can be mixed further to create additional shades.
Tertiary colors are the result of a primary and secondary color mixed together. For example, orange mixed with red creates red-orange.