Nedarim, Chapter 4, Mishnah 3. The Mishnah continues to discuss a person who vowed not to derive benefit from his fellow, and it details which things his fellow may still do for him. Throughout the lesson we will use the following example: Reuven is the one bound by the vow, forbidden to derive benefit from Shimon, and Shimon is the one who is forbidden to provide him with benefit.
Separating Terumah and tithes:
The Mishnah opens: "Mafrish es terumaso u'maasrosav l'daato" - Shimon may separate Terumah and tithes from Reuven's produce, provided that it is done "l'daato," that is, with Reuven's knowledge.
Reuven may not instruct Shimon directly to separate on his behalf, for then Shimon would be acting as his agent, and fulfilling the request would count as a favor and a benefit for Reuven. But he may say in general terms: "Whoever wishes to separate may separate," and on the strength of such a statement Shimon is permitted to do so.
The commentators explain that this ruling applies specifically when Shimon separates from Reuven's own grain and produce. But when Shimon separates from his own for his own, he does not need Reuven's knowledge or consent at all, since this is nothing but an advantage for him.
Offering sacrifices in the Beis HaMikdash:
If Shimon is a kohen, then even though Reuven is forbidden to derive benefit from him, Shimon may offer sacrifices on his behalf in the Beis HaMikdash:
"Kinei zavim v'kinei zavos" - the bird offerings of a zav and of a zavah.
"Kinei yoldos" - the bird offerings that a woman who has given birth is obligated to bring.
"Chataos va'ashamos" - a sin offering and a guilt offering, as well as the other sacrifices.
The Mishnah specifically chose these sacrifices because they all permit a person to eat sacred foods, so that the benefit they provide is more direct. Even so it is permitted, because the kohanim are agents of Heaven and not agents of the owners of the sacrifices, and Reuven receives from Shimon nothing more than indirect benefit.
Torah study:
Shimon may teach Reuven:
"Midrash" - the halachic Midrashim: the Mechilta, the Sifra and the Sifri, from which we learn how the laws of the Oral Torah are derived from the Written Torah.
"Halachos" - the study of practical halachah.
"Aggados" - the aggadic and philosophical portions of the Torah.
But "lo yelamdenu mikra" - he may not teach him Chumash free of charge. The reason is that in the other areas of Torah a teacher is not halachically entitled to take payment for his teaching, whereas for teaching Scripture one may take payment. This is because in teaching Scripture one also teaches the punctuation of the cantillation and the melody, and to that the teacher is not obligated, and therefore he was permitted to receive payment. It follows that teaching Scripture free of charge is a real benefit.
"Aval melamed hu es banav v'es benosav mikra" - Shimon may teach Reuven's sons and daughters Scripture. Although it is a mitzvah for a father to teach his son Torah, so that Shimon is filling Reuven's need, this is not considered a benefit, since he is merely fulfilling a mitzvah in his place, and mitzvos were not given for the purpose of deriving benefit.
Supporting his wife and children:
"V'zan es ishto v'es banav" - Shimon may provide food for Reuven's wife and children, even though Reuven is the one obligated to support them. The reason is learned from the previous Mishnah: one may pay off the debt of a person bound by a vow, and this is nothing more than the repayment of a debt.
Feeding his animal:
"V'lo yazun es behemto, bein temeiah u'vein tehorah" - Shimon may not feed Reuven's animal, whether it is a non-kosher animal or a kosher one, since fattening the animal is a full-fledged benefit for Reuven.
Rabbi Eliezer draws a distinction and says: "Zan es hatemeiah v'eino zan es hatehorah" - the non-kosher animal may be fed, but not the kosher one, since Reuven will eventually slaughter the kosher animal and derive direct benefit from the food it was fed.
The Sages said to him: "Mah bein temeiah litehorah?" - what basis is there for this distinction? He said to them: "Shehatehorah nafshah lashamayim v'gufah shelo" - with a kosher animal, its soul and life force go up to Heaven once it is slaughtered, but its body is his, and he can eat its meat and benefit from its having been fattened. With a non-kosher animal, however, both its soul and its body belong to Heaven, and Reuven can do nothing with it, so he does not benefit from its having been fattened.
The Sages answered him: "Af temeiah nafshah lashamayim v'gufah shelo" - for with a non-kosher animal too the body is his, since if he wishes he can sell it to non-Jews or feed it to dogs. It turns out that fattening the non-kosher animal of the one bound by the vow also involves benefit, just as fattening his kosher animal does.
In summary: in this Mishnah we learned which things may be done for someone who is forbidden to derive benefit: separating Terumah and tithes with his knowledge, offering his sacrifices through a kohen, who is an agent of Heaven, teaching him Midrash, halachos and aggados (but not Scripture, for which payment is taken), teaching Scripture to his sons and daughters on the principle that mitzvos were not given for the purpose of deriving benefit, and providing food for his wife and children on the principle of repaying a debt. Feeding his animal, by contrast, is forbidden, and Rabbi Eliezer and the Sages disagree about whether there is benefit in the case of a non-kosher animal.