A whole comprises all its parts. All the parts together compose the whole.
To comprise is to consist of. A dozen eggs comprises 12 eggs. The USA comprises 50 states (plus territories & whatnot).
To compose is to make up, in the sense that twelve eggs make up a dozen. A mother, a father, & their offspring compose a typical nuclear family.
Many people misuse "comprise" where they mean "compose". They turn the meaning of "comprise" inside-out by improperly using the passive voice, thus: "A deck is comprised of 52 cards." The correct usage is: "A deck comprises 52 cards" OR "A deck is composed of 52 cards."