(Mishnah): Hotza'os of Shabbos are two that are four inside, and two that are four outside;

How is this? An Oni (poor person) is standing outside [in a Reshus ha'Rabim], and a Ba'al ha'Bayis is inside [his house, a Reshus ha'Yachid]. If the Oni [was holding an object, and] sticks his hand inside and puts in the Ba'al ha'Bayis' hand, or he takes from [the Ba'al ha'Bayis'] hand and takes it outside, the Oni is Chayav [Kares if he was Mezid, Misah if he was warned, and Chatas if he was Shogeg], and the Ba'al ha'Bayis is exempt;

If the Ba'al ha'Bayis [was holding an object, and] sticks his hand outside and puts in the Oni's hand, or takes an object from [the Oni's hand] and takes it inside, the Ba'al ha'Bayis is liable, and the Oni is exempt;

If the Oni [was holding an object, and] sticks his hand inside and the Ba'al ha'Bayis took it from him, or [the Ba'al ha'Bayis] put in [the Oni's] hand and he takes it outside, both of them are exempt;

If the Ba'al ha'Bayis [was holding an object, and] sticks his hand outside and the Oni took it from him, or [the Oni] put in [the Ba'al ha'Bayis'] hand and he takes it inside, both of them are exempt.

(Gemara) Question: What are "two that are four''? [Does it mean] two for Chiyuv [full Hotza'ah, i.e. Akirah and Hanachah, and full Hachnasah], and two for Petur (Akirah alone or Hanachah alone, whether for Hotza'ah or Hachnasah)?

Or, [does it mean two that are] four for Chiyuv [the Ba'al ha'Bayis did Hotza'ah or Hachnasah, and likewise for the Oni], and four for Petur (the Ba'al ha'Bayis did Akirah alone or Hanachah alone, and likewise for the Oni)?

Answer #1: We learn from a Mishnah (Shevu'os 1:1). There are two Shevu'os, which are four. (Surely there are not eight! Rather, the first Perush is correct.)

Rebuttal (R. Ba): There (Shevu'os), all of them are liable. However, here (Shabbos) it comes to teach Chiyuv and Petur. [We can explain that our Mishnah] says that four are for Chiyuv, and four for Petur.

Support (for Rebuttal - R. Yosi): The Mishnah [in Shevu'os] teaches so! There are two Shevu'os which are four. Are not all for Chiyuv?! (Surely they are!) Similarly, Yetzi'os ha'Shabbos are two that are four - is this not to be liable?!

Question: It was taught "there are two doors of the Heichal, which are four.'' Can you say that they are for Chiyuv or Petur?! (R. Yosi's support is unfounded. We explained this like PNEI MOSHE.)

Question: [Our Mishnah] should teach 12 cases of Petur! (There are four Akiros in which the other person did the Hanachah - in every case, both of them are exempt. There are also the four cases in our Mishnah in which one did the entire Melachah and is liable, and the other was totally passive, and he is exempt.)

Answer #1: It teaches only exemption similar to the cases of Chiyuv (he brought something in or out, but he is exempt because he did not do the Akirah or Hanachah).

Answer #2 (R. Chiya bar Rav Ada bar Ahavah): What are the cases of exemption taught? When it is permitted (he was totally passive, and the other person did the entire Melachah. There are four such cases. It is permitted regarding Shabbos; it is forbidden due to Lifnei Iver.)

(R. Yosi): Oni and Ashir are the same (both are liable when they do the entire Hotza'ah or Hachnasah), and Chachamim counted them like two (because Hotza'ah is an inferior Melachah, we would not have learned one from the other);

Hachnasah and Hotza'ah are one [Melachah], and Chachamim counted them like two.

Source #1: [The Mishnah taught] Yetzi'os of Shabbos - is Hachnasah not included?! (Surely it is!) [The Mishnah that lists the Melachos taught] "one who is Motzi from Reshus to Reshus'' - is Machnis not included?!

Source #2: R. Yosah taught in the name of R. Yochanan that one who entered half a Grogeres (the Shi'ur of food for which one is liable) and took out half a Grogeres is liable.