Mishnah 6 in Chapter 14 continues directly from where the previous Mishnah left off: once the Mishkan was moved from Gilgal to Shiloh, bamot were once again prohibited.
The structure of the Mishkan in Shiloh:
The structure erected in Shiloh did not have a stone roof, but was covered with tapestries - the same fabric used on top of the Mishkan in the wilderness. The base was built of stones, and the tapestries were spread over it. According to the Yerushalmi, the stones reached a height of ten handbreadths, and the original Mishkan of the wilderness was placed upon them.
The "menuchah" in the verse:
As we mentioned at the beginning of the chapter, in the words of Moshe Rabbeinu from which the permission for bamot is derived, it says: "Ki lo basem ad atah el hamenuchah ve'el hanachalah" - "menuchah" is the resting place, and "nachalah" is the inheritance. The Mishkan in Shiloh was erected during a period of stability and stood there for three hundred and sixty-nine years; the Jewish people ceased their wanderings and their conquest of the Land and settled in it. This is the "menuchah" in the verse, and from the moment they reached it, the prohibition to offer sacrifices on bamot took effect.
The sacrifices in the Mishkan of Shiloh:
From now on, not only communal sacrifices were brought, but also the private sacrifices of the individual: someone who was obligated to bring a chatas brought it to the Mishkan in Shiloh, which was not possible in Gilgal. The meat of the chatas - as well as communal chatas offerings, such as the he-goats of the musaf, along with asham offerings and menachos - was eaten "lifnim min hakela'im" - inside the curtains: curtains were spread around the courtyard of the Mishkan in Shiloh, and within them was the place where they were eaten.
Kodashim kalim and ma'aser sheni:
Kodashim kalim - these were eaten "bechol haro'eh" - in any place that sees, meaning anywhere from which the Mishkan in Shiloh could be seen. This law differs from the law of Jerusalem, where the wall is the boundary, as we learned in the previous Mishnah. Its basis is in a verse, by way of derivation or asmachta, and in practice, this was the law and this is how they applied it there.
Ma'aser sheni - this is the tithe separated in the first, second, fourth, and fifth years of the Shemitah cycle, and the place it is eaten is within the walls of Jerusalem. As long as there was no Jerusalem, its corresponding place was the same place where kodashim kalim were eaten - within the line of sight of the Mishkan in Shiloh.
If the question is asked why ma'aser sheni has not been mentioned until now, the answer is that until the completion of the conquest and division of the Land of Israel, those fourteen years, there was no obligation to separate Terumah and tithes. Once the process was completed, the obligation of Terumah and tithes took effect, including ma'aser sheni - and during the three hundred and sixty-nine years that the Mishkan stood in Shiloh, it had to be eaten within the line of sight of Shiloh.
In summary: In this Mishnah we learned about the Mishkan that was erected in Shiloh - a base of stones up to ten handbreadths and the tapestries of the Mishkan above it - which is the "menuchah" in the verse, and because of this, bamot were prohibited. Kodesh kodashim, asham offerings, and menachos were eaten "lifnim min hakela'im" - inside the curtains, whereas kodashim kalim and ma'aser sheni were eaten "bechol haro'eh" - anywhere from which the Mishkan in Shiloh could be seen.