The Megillah is read on the 11th etc... - Sometimes on this and sometimes on this, and further it will be explained

Not less and not more - Not before the 11th and not later than the 15th.

From the days of Yehoshua - In the Gemara it will be explained

But villages move forward to the day of entry - Which is to say, since the walled cities read on the 15th, and since the walled cities do not read on the 14th, behold in all, where is it found (that we read on) the 11th, the 12th, the 13th? But the Sages gave to villages permission to push forward their reading to the day of entry. The second day from Shabbat (Monday) which would fall before the 14th, or the fifth day from Shabbat (Thursday), which is a day of entry for the villages, whom enter into the cities for judgment (court cases) before the Beit Dinim (Courts) which dwell in the cities on Mondays and Thursday, as was decreed by Ezra (see Bava Kama page 82). And the villages are not experts in reading, and need one of the men of the city to read for them, and the Sages didn't burden them to make them come later, so they come on the day of the 14th and sometimes on the day of entry on the 13th and sometimes it is the 11th.

Should the 14th fall on Erev Shabbat (Friday), large cities and walled cities will read on that day (Friday) - For there is no Megilah reading on Shabbat due to a Gezeira (Rabbinical legislation to prevent the violation of a biblical commandment) for perhaps one may come to carry it (the Megilah) in his hand (and thereby violate the Sabbath). If you should say that walled cities should delay until Sunday, that would be the 16th and the Megilah states that the time for reading the Megilah should not go past the 15th.

Should (the 14th of Adar) begin on Sunday, villages will move their reading up to the previous Day of Assembly (Thursday) - This will be the 11th (of Adar) and we don't find a Day of Assembly that is before Purim that is earlier than that because we do not advance the Megilah reading from one Day of Assembly to the previous Day of Assembly.

Gemara: This is the correct version of the text: From where is it derived? (What kind of questions is) From where!? It's like we mean to say later etc. - And here is the meaning: From where is it derived that the 11th, 12th, and 13th are appropriate days for reading (the Megilah)? For (only) the 14th and 15th are written in the Bible (Megilat Esther). The Gemara retorts by asking "From where is it derived?" with astonishment. This is not obligatory rather the Sages provided a leniency as we shall see later on.

In order that they may provide - So that they will be available on Purim to provide for the needs regarding the Purim feast to the residents of the large cities.

This is what we mean to ask - We who are asking "From where is it derived (that the Megila may read on 11th, 12th, or 13th under certain circumstances)? This is what we mean:

Let's analyze the situation - since the Sages provided a leniency to the villagers to read early, of necessity you must therefore conclude that the Men of the Great Assembly who established the festivities of Purim and the reading of the Megila in the days of Mordechai and Esther must have established all of these days (11th, 12th, and 13th along with the explicitly stated 14th and 15h) and given permission to read (the Megila on those days).

Because if you should think - the 14th and 15th are established in writing in the Megila and no more (i.e. no other dates).

How could the Rabbis come - How could (the Rabbis) that came after them (the Men of the Great Assembly) and uproot their enactment and give permission for (villagers) to read earlier (than the 14th)! (read with with astonishment):

...A time of assembly - Everyone assembled to avenge from their enemies, whether in Shushan or other places as it is written in the book, therefore, the passuk does not need to include the 13th day as a day for reading the Megilla because the essence of the miracle happened on that day.