The Final Decision was a 2268 plan by the Ekosian Nazi party to attack Zeon, the next planet out from Ekos in its system, by means of its space fleet consisting of both manned and unmanned weapons. The party's new slogan "Death to Zeon" also sanctioned the "elimination"--the imprisonment, torture and execution, if not the outright beating to death on the street--of the Zeons who had resided on Ekos for half a century.
The Final Decision was halted at the last minute by the intervention of a Starfleet landing party who arrived to examine the situation. Although Zeon/Ekosian resistance pleaded with Capt. James Kirk to order his ship to destroy the invasion fleet, the officer decided on a better solution. That came with a combination of McCoy's injection, Spock's "mind probe", and then another injection and a slap from Captain Kirk to bring the near-comatose Federation cultural observer John Gill to his senses. Finding the will to seize the power of command he had expected when he first assumed the title "Führer", Gill made this speech:
- "People of Ekos. Hear me. We were betrayed by a self-seeking adventurer who has led us all to the very brink of disaster. I order the immediate recall of the space fleet. This attack must stop. All units are to return to base. To Zeon I promise this was not an aggression of the Ekosian people, only one evil man. Melakon is a traitor to his own people and all that we stand for. To the Zeon people I promise reparation..." At this point, Melakon grabbed a machine gun and opened fire on Gill, eventually killing him.
The toppling of Deputy Führer Melakon and the rescinding of his evil plan were fairly straightforward, as both Party Chairman Eneg (who, after Melakon was killed by Isak, a Zeon disguised as a Nazi, prevented a pro-Melakon solider from retaliating) and Party Secretary (and Hero of the Fatherland) Daras were secretly agents of the anti-war underground. (TOS: "Patterns of Force")
The Zeon Isak uses the Earth history term "Final Solution" to describe the Führer's formal declaration of war against his people. In the Chancellery that evening, Kirk too prefers the Earth term, referring to "the Führer's Final Solution speech."
The USS Enterprise, being mistaken for an attacking Zeon spacecraft, would seem to have given the Deputy Führer an excuse to launch his Final Decision. (Nazi media also misreported her self-defensive destruction of their warhead-bearing missile, pretending that the Ekosian device "utterly destroyed" its alien target.) However Kirk and Spock have already witnessed anti-Zeon police violence when they see on public viewscreen as back-to-back news items the alien spacecraft incident and the announcement of the Final Decision to render the "glorious" planetary capital "Zeon-free".
After preventing Melakon's henchman from killing Isak, Eneg said that Ekosians would now live as "the way the Führer meant us to live" - this would suggest that, while its genocidal policies were removed, the Nazi system may well have remained in place.