Kilayim, Chapter 4, Mishnah 2. In the previous Mishnah we encountered the concept of "mechol hakerem", and we learned that according to Beis Shammai a gap of sixteen amos is required in order to be permitted to sow in that area, while according to Beis Hillel twelve amos are required.
What is mechol hakerem?
Our Mishnah explains what was mentioned in the previous Mishnah: mechol hakerem is the gap between the vineyard and the fence. If there are not twelve amos there (according to Beis Hillel), one may not bring seeds there and may not sow in it at all. But if there are twelve amos between the vineyard and the fence, we give the vineyard its "avodaso" - the four amos adjacent to it, in which one does not sow - and the rest may be sown.
The calculation of the twelve amos according to Beis Hillel:
Four amos adjacent to the vineyard - the working space of the vineyard, in which sowing is forbidden.
Four amos for a field - this is the minimum measure for the area to be considered a field in which one can sow. Less than that is insignificant and is considered subordinate to the vineyard.
Four amos adjacent to the fence - since it is the way of people not to sow there.
True, one is permitted to plant in the area adjacent to the fence if it has the appropriate measure of distance, but the usual practice is not to view it as part of the functional field, because it is left to the side so that people can walk through it, and also because it adds strength to the ground next to the fence. Altogether the calculation comes to twelve amos according to Beis Hillel.
The calculation according to Beis Shammai:
According to Beis Shammai, as was mentioned in the previous Mishnah, in order for the area to be considered a field that is not subordinate to the vineyard, eight amos are required, and not four as Beis Hillel hold. Accordingly the calculation is:
Four amos adjacent to the vineyard - the working space of the vineyard.
Eight amos, so that the area will be considered a field and will not be subordinate to the vineyard.
Four amos adjacent to the fence.
In summary: In this Mishnah we learned that mechol hakerem is the gap between the vineyard and the fence, and that in the absence of the required measure one may not bring seeds there at all. When the measure is present, we give the vineyard its working space and sow the remainder. We went through the details of the calculation: for Beis Hillel, twelve amos (four for the working space of the vineyard, four for the measure of a field, and four adjacent to the fence), and for Beis Shammai, sixteen amos, since in their view eight amos are required for the area to be considered a field that is not subordinate to the vineyard.