Eternal Death and Annihilation are not the same doctrines. Annihilation is being winked out of existence, as if removed from all reality. That is not Bible. Rather, eternal death is the punishment for dying in unrighteousness before a Holy God.
The dead, saint and sinner alike, await the resurrection. For the saint, resurrection of the just occurs and is the first resurrection, over which the second death has no power. They are granted eternal life, that is, permanent immortality.
For the rest of the dead, they experience the resurrection of the unjust and are brought before the throne for judgment. All those found wanting according to their works are cast into the lake of fire. This is the second death. They are granted eternal death, that is, permanent mortality.
They are not annihilated anymore than if you took a corpse and reduced it to bone chips and ashes. Merely the form of the matter has changed, but it still exists as matter.
Similarily, the second death reduces sinners to everlasting destruction, from which there is no recovery, but it doesn't wink them out of existence.
The quotes from
Mark 9 from the Lord Jesus regarding the fire that is not quenched and the maggots (thanks, Bro EB!) that do not die is from
Isaiah 66. There we are told that the corpses of the unrighteous are seen. They are abhorrent to the living. There bodies are riddled with maggots who feast of their dead flesh. They are disposed of in Jerusalem's garbage heap, Gehenna, which was perpetually set on fire to burn away the uncleanness of the area.
In no way were these corpses annihilated into non-existence. Rather, they were former living humans who have died and been dumped by judgment into the hell-hole assigned to the unrighteous.
They are forever dead, even as maggots feast on and lay their eggs in, their rotting corpses.
This is what the Lord Jesus refers to. He didn't teach annihilation. He taught eternal death. Those who suffer the second death are literally dead, reduced to being deprived of all consciousness, and therefore "know nothing". But they are still an abhorrence to the living righteous.