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וְרָחֲצ֛וּ אַהֲרֹ֥ן וּבָנָ֖יו מִמֶּ֑נּוּ אֶת־יְדֵיהֶ֖ם וְאֶת־רַגְלֵיהֶֽם׃

И Аарон и его сыновья помоют руки и ноги их на этом;

English Explanation of Mishnah Zevachim

All sacrifices whose blood was caught by a: non-priest, an onen, a tebul yom, one lacking [priestly] vestments, one lacking sacrificial atonement, one who had not washed his hands and feet, an uncircumcised [priest]; an unclean [priest]; one who was sitting, one who was standing on utensils or on an animal or on another’s feet, are disqualified.
If [the priest] caught [the blood] with his left hand, it is disqualified. Rabbi Shimon declares it valid.
If the blood was poured out on to the pavement and [the priest] collected it, it is disqualified.
If [the priest] put it [the blood] on the ramp [to the altar], [or on the altar, but] not against its base; if he applied [the blood] which should be applied below [the scarlet line] above [it] or that which should be applied above, below, or that which should be applied within [he applied] without, or that which should be applied without [he applied] within, it is invalid, but does not involve karet.

Section one: This is a list of people who cannot receive the blood of a sacrifice in a vessel, or carry it to the altar, or sprinkle it on the altar. Note that the mishnah does not say that these people cannot slaughter the animal. The laws regarding slaughtering the sacrifice are less strict. I shall explain each category one at a time:
Non-priest: only priests can perform these activities.
An onen: Someone who had one of their close relatives die is considered an onen on the day of the death.
A tebul yom: This is the word for an impure person who has immersed in a mikveh but before the end of the day (before the sun sets after he was made pure). See Leviticus 22:7. Believe it or not, there is an entire tractate in Seder Toharot devoted to this subject.
One lacking [priestly] vestments: A regular priest must wear four garments and the high priest must wear eight garments (see Yoma 7:5). Without the proper attire, the sacrifice is invalid.
One lacking sacrificial atonement: In certain cases, when one’s period of impurity is over he must bring a sacrifice. If the priest has not brought the required sacrifice, he cannot take part in the sacrificial worship.
One who had not washed his hands and feet: See Exodus 30:19.
An uncircumcised [priest]: See Ezekiel 44:9.
An unclean [priest]: one must be ritually pure to offer sacrifices.
One who was sitting, one who was standing on utensils or on an animal or on another’s feet, are disqualified: the sacrificial procedure must be performed while standing on the floor of the Temple’s courtyard, not sitting or standing on something else.
Section two: According to the first opinion, the blood must be caught in one’s right hand. Rabbi Shimon says it can be caught in the left hand.
Section three: The blood has a very specific place upon which it must be poured. It cannot be poured on the floor of the Temple, or on the ramp leading up to the Temple. It must be applied to the base of the altar. Sometimes the blood must be poured on the lower part of the base, which was separated by a crimson line from the upper part, and sometimes it must be poured on the upper part. The important thing is that the blood is poured on the part appropriate to that sacrifice. If it is not, the sacrifice is invalid. Similarly, sometimes the blood must be poured on the altar inside the Sanctuary (the Hekhal) or even within the Holy of Holies, and at other times it must be poured on the outer altar. What again is essential is that the blood of each sacrificed is poured on the altar upon which it is supposed to be poured. If it is not, the sacrifice is invalid.
Although this sacrifice is invalid, one who eats of its flesh is not liable for karet (a biblical penalty of great severity) unlike one who eats of one of the sacrifices disqualified in mishnah two or three. In those cases, when the animal was sacrificed with the wrong intent, eating its flesh was punished by the serious penalty of karet.

English Explanation of Mishnah Menachot

As for both a sinner’s minhah and any other minhah if [one of the following] removed the handful: a non-priest; or [a priest] that was an onen; or one who immersed himself during the day; or was not wearing the priestly vestments, or whose atonement was lacking; or who had not washed his hands and feet; or that was uncircumcised; or unclean; or was sitting, or standing upon vessels or upon a beast or upon another's feet, it is invalid. This section contains a list of cases in which a priest who removes the handful from the minhah renders it invalid. The same list appears in Zevahim 2:1, so I am basically replicating my commentary here: Non-priest: only priests can perform these activities. An onen: Someone who had one of their close relatives die is considered an onen on the day of the death. A tebul yom: This is the word for an impure person who has immersed in a mikveh but before the end of the day (before the sun sets after he was made pure). See Leviticus 22:7. One lacking [priestly] vestments: A regular priest must wear four garments and the high priest must wear eight garments (see Yoma 7:5). Without the proper attire, the minhah is invalid. One lacking sacrificial atonement: In certain cases, when one’s period of impurity is over he must bring a sacrifice. If the priest has not brought the required sacrifice, he cannot take part in the sacrificial worship. One who had not washed his hands and feet: See Exodus 30:19. An uncircumcised [priest]: See Ezekiel 44:9. An unclean [priest]: one must be ritually pure to offer sacrifices. One who was sitting, one who was standing on utensils or on an animal or on another’s feet, are disqualified: the sacrificial procedure must be performed while standing on the floor of the Temple’s courtyard, not sitting or standing on something else.