Parah, Chapter 7, Mishnah 3. This chapter is occupied with the melachah that ruins the water of the parah adumah. Water drawn for the mei chatas must be handled with undivided attention: if the person busy with it turns aside to some other labor, the water is disqualified. A central point emerges from our Mishnah: a man's melachah spoils only his own water. Water that belongs to somebody else is not affected by what he does with his other hand.
Begin with a man whose two hands are busy at the same moment. The Mishnah's words are "Hamikadesh b'achas yado", he sprinkles the ashes onto the water, performing the kiddush, using only one hand, and meanwhile, "v'oseh melachah b'achas yado", his second hand is occupied with some unrelated labor. What becomes of the water? The Mishnah answers with a distinction. "Im lo, pasul": should the water belong to him, it is ruined, for a melachah accompanied his handling of his own mei chatas. "V'im l'acher, kasher": should the water be the property of a different man, the kiddush holds good, for one person's labor cannot spoil water he does not own.
The next case: "Hamikadesh lo u'le'acher", he performs the kiddush for himself and for another man. Here the ruling splits: "shelo pasul v'shel acher kasher", the water that is his own is invalid, while his fellow's water remains valid. Once again the same measure applies: the melachah he did alongside his own sanctification ruins what belongs to him, and leaves untouched what belongs to somebody else.
And the closing case. "Hamikadesh lishnayim k'echad" describes a man sanctifying water for two other people in a single act, and the verdict is "shneihem k'sheirin", both quantities of water are fit. The reasoning follows directly from what came before: not one drop of this water is his, so his occupation with the second portion cannot ruin the first, nor the reverse. The rule that would have ruined water of his own has nothing to attach itself to when both parties he serves are other men.
The Mishnah thus draws a clear line. The disqualification of melachah is a private matter, attaching to the owner of the water and to nobody else. When a man works on behalf of others alone, even simultaneously and even with both hands occupied, the mei chatas he prepares is fit.