Comprise means “to be composed of” or “to contain.” Constitute means “to be one of the parts of” something. You could say that the parts constitute the whole and the whole comprises the parts.
According to the traditional rule, the whole comprises the parts. The parts, on the other hand, compose the whole or constitute the whole or make up the whole. Thus:
The USA comprises 50 states. Fifty states compose the USA.
Fifty states constitute the USA.
Fifty states make up the USA.
According to Bryan Garner, however, the expression is comprised of is “always wrong and should be replaced by some other, more accurate phrase….” Garner, Oxford, p. 75.
Example: Coca-Cola comprises many substances, which constitute the secret formula.