The gemarah determines that Zechirah is B'peh, therefore the megillah must be said B'peh, but it does nothing to prove that the megilah can not be said Baal Peh.
The gemarah then moves on. What is the final determination of the question Minalan that it can't be said Baal Peh?
m. Zians, Hamilton,Canada
1) Before the Gemara determined that Zechirah is b'Peh, it had already proved that it cannot be said Ba'al Peh.
2) The Gemara learns the latter from the word "Nizkarim" used in Esther 9:28. Since the root of the word "Nizkarim" is Zechirah, the Gemara makes a Gezeirah Shavah between here and the word "Zikaron" used in Shemos 17:14. Since Shemos 17:14 says that Zikaron comes about through a book, it follows that the "Nizkarim" mentioned in Esther also has to be through a book, which is how we know that the Megilah cannot be said Ba'al Peh.
3) The Gemara then continues with a new question. We know that we have proved from "Nizkarim" that one must have a book, and it is not sufficient to say it by heart. But once one has a book, or scroll, how do we know that it is not sufficient to read it silently from the scroll? How do we know that one must read the Megilah out loud? For that the Gemara cites a different Limud to prove that whenever the word "Zachor" is used by the Torah, this means that it is not sufficent to "remember" it in one's head, but rather the word "Zachor" means that one must "mention" it out loud.
4) However, the original question, "Menalan" -- how does the Mishnah know that Ba'al Peh, saying it by heart, is unacceptable -- was answered right at the beginning when the Gemara brought the Gezeirah Shavah.
Kol Tuv,
Dovid Bloom
But isn't there a klall that you can't learn 2 halachos from the same word?
We are not learning two Halachos from the same word.
1) We know from the word "Nizkarim" in Esther 9:28 that we require "Zechirah" for Megilas Esther. Now we proceed to define two aspects of what this Zechirah entails: (a) It should not be Ba'al Peh but should be read from a scroll; (b) It should be said out loud, b'Peh.
2) Aspect (a) is derived from the Gezeirah Shavah to "Zikaron" in Shemos 17:14. Aspect (b) is derived from the word "Zachor" in Devarim 25:17, that whenever the Torah says "Zechirah" about something, it means that it must be out loud.
3) Accordingly, we have taken the word "Nizkarim" and used two other words ("Zicharon" in Shemos 17:14, and "Zachor" in Devarim 25:17) to explain two details applicable to "Nizkarim." This means we learned two things from two different words.
B'Hatzlachah Rabah,
Dovid Bloom