Mishnayos Zevachim Perek 10 Mishnah 2

Any offering that is more sacred than another precedes the other offering. The mishna elaborates: If there is blood of a sin offering and blood of a burnt offering to be presented, the blood of the sin offering precedes the blood of the burnt offering because it effects acceptance, i.e., atonement, for severe transgressions punishable by karet. Likewise, if there are limbs of a burnt offering and portions of a sin offering to be burned on the altar, the burning of the limbs of the burnt offering precedes the portions of the sin offering, because the burnt offering is entirely burned in the flames on the altar, whereas only part of the sin offering is burned. Similarly, although both effect atonement, a sin offering precedes a guilt offering due to the fact that its blood is placed on the four corners of the altar and the remnants of its blood are poured on the base of the altar, whereas the blood of the guilt offering is sprinkled on only two corners of the altar. A guilt offering precedes a thanks offering and the nazirite’s ram due to the fact that it is an offering of the most sacred order, and the others are offerings of lesser sanctity. A thanks offering and a nazirite’s ram precede a peace offering due to the fact that they are eaten for one day, like offerings of the most sacred order, whereas a peace offering is eaten for two days, and the thanks offering and nazirite’s ram require loaves to be brought with them, four types with the thanks offering and two types with the nazirite’s ram. Sacrifice of the peace offering precedes sacrifice of the firstborn offering due to the fact that the peace offering requires placing the blood on the altar, in the form of two placements that are four, and placing hands on the head of the offering, and libations, and the wavings of the breast and the thigh by the priest and the owner; none of which is required for the firstborn offering.