Eruvin, Chapter 6, Mishnah 10. This mishnah continues the ideas of the previous mishnah, and it is presented according to the view of the Tanna Kamma there, that a foot which is prohibited in its own place prohibits in a place that is not its own: if the inner courtyard is prohibited because it did not make an eruv, the outer courtyard is prohibited as well, since the residents of the inner one pass through it; but if the inner courtyard is permitted, such as when it made a proper eruv, the outer one is not prohibited.
Each courtyard made an eruv for itself:
"Shachach echad min hachitzonah velo eirev" - one of the residents of the houses in the outer courtyard did not join the eruv, and thereby ruined it, so that the outer courtyard has no valid eruv. In this case the inner courtyard is permitted and the outer one is prohibited: the inner courtyard made a proper eruv and is therefore permitted, while the outer one is prohibited since one of its residents forgot and its eruv is void.
"Min hapenimit velo eirev" - both are prohibited. Since one of the residents of the inner courtyard did not join the eruv, the inner courtyard is prohibited in carrying from the houses into the courtyard, and since its residents have right of passage through the outer courtyard, the outer one is prohibited as well - a foot which is prohibited in its own place prohibits in a place that is not its own, according to the Tanna Kamma of the previous mishnah, whose view we are following.
They placed their eruv in one place:
Here the two courtyards join together and make a single eruv, and the eruv is placed in one place. The Gemara explains that "one place" means the area common to both of them, which is the outer courtyard, since the residents of the inner courtyard pass through it. It turns out, then, that the eruv shared by both courtyards was placed in the outer courtyard.
And in that same case: "Veshachach echad, bein min hapenimit bein min hachitzonah" - if one of the houses did not join the eruv, it makes no difference whether the one who forgot is from the inner courtyard or from the outer courtyard, and both courtyards are prohibited.
The reason is this: since the eruv is placed in the outer courtyard, even if the one who forgot is from the outer courtyard, the residents of the inner courtyard cannot lock their door and say, "We will keep our courtyard to ourselves, and you on the outside have become prohibited." Since the eruv of the inner residents is placed in the outer courtyard, they must contend with the fact that the outer courtyard is prohibited on account of the one who forgot, and therefore they too are prohibited.
The eruv was placed in the inner courtyard:
In contrast to the case of our mishnah, if the eruv is placed in the inner courtyard and one of the residents of the outer courtyard forgot, the residents of the inner courtyard can, as it were, lock their door and say, "We are permitted on our own, and you on the outside have a problem" - and in this scenario the inner courtyard is permitted. But if one of the residents of the inner courtyard forgot, the outer courtyard is prohibited as well, since we are following the view of the Tanna Kamma of the previous mishnah, that when the inner courtyard is prohibited the outer one becomes prohibited along with it - just as in the case of our mishnah, where the eruv is placed in the outer courtyard.
If the two courtyards belonged to individuals:
The mishnah concludes with a case in which there was only a single house in each of the courtyards. Here there is no one to make an eruv with within each courtyard, since each courtyard belongs to an individual, and they also do not need to make an eruv with one another - for this is a case of a foot that is permitted in its own place. The individual in the inner courtyard is permitted, since there is no one else with him, and since he is permitted, even though he passes through the outer courtyard he does not prohibit it, as long as the inner courtyard is permitted in its own right. All of this is according to the view of the Tanna Kamma of the previous mishnah, and not like Rabbi Akiva there, who holds that even in this case there is a problem.