For I have known them all already, known them all:— Have known the evenings, mornings, afternoons, I have measured out my life with coffee spoons; I know the voices dying with a dying fall Beneath the music from a farther room. So how should I presume?
Now he’s trying to convince us that he’s a wise man with lots of experience. He doesn’t need to do anything, because he’s done everything already!
And by "done everything," we mean he has survived "evenings, mornings, afternoons." Impressive.
What else have you done, Prufrock? Well, he has drank a lot of coffee – in fact, his whole existence can be "measured" by how much coffee he has drank.
This is a wicked image. Prufrock thinks he is impressing us, but he’s really damning himself before our eyes. He basically lives from one cup of coffee to the next, with nothing interesting in between.
Prufrock says he has heard voices "dying" or fading away when music starts to play in a "farther room." We already know that he has a hard time entering rooms that contain people he wants to talk to (see lines 37-39), so he has to settle on overhearing other people’s voices through the walls. He lives through other people.
The phrase "dying fall" is, you guessed it, another literary reference, this time to Shakespeare’s famous play, Twelfth Night. In the first scene of the play, a lovesick count named Orsino is listening to music that has a "dying fall." The music reminds him of his love for one of the other characters.
In this poem, however, it’s as if Prufrock were overhearing the "voices" of another couple – maybe Orsino and his love? – in another room, which get covered up by yet another room even "farther" away.
It’s a tricky image, we know, but the point is that Prufrock can only experience love at second- and third-hand. If Orsino’s love is the real thing, then Prufrock’s is just a copy of a copy of a copy.
Finally, he asks, "So how should I presume?" To "presume" is to take for granted that something is the case. The speaker of Andrew Marvell’s "To His Coy Mistress" presumes that his mistress wants to sleep with him.
This can be a bad thing, if you presume too much, but Prufrock is just looking for any reason not to ask his important question. He doesn’t want to "presume" that he’ll get a favorable response. This is pretty cowardly of him.