Learn Hardcore Turkish: Sunumu çeyrek saat uzatabilir miyiz, yoksa mola mı verelim? - Can we extend the presentation by a quarter of an hour, or shall we take a break?

Because uzatmak is a transitive verb and the object is specific/definite. In Turkish, definite direct objects take the accusative: sunumu = “the presentation (acc.)”. Without -u, sunum would be interpreted as an indefinite object (“a presentation”), which doesn’t fit here.

Does sunumu mean “my presentation”? I’m confused by the ending.

No.

sunumum = “my presentation” (1st person singular possessive)
sunumu = “the presentation” (accusative of “sunum”)
sunumumu = “my presentation” in the accusative So in the sentence, sunumu is just the definite object.

Is çeyrek saat the same as “15 minutes”? Do I need bir?

Yes, çeyrek saat = “a quarter of an hour” = 15 minutes. You normally do NOT add bir here; bir çeyrek saat sounds bookish or mathematical. You can also say on beş dakika, which is very common and neutral.

Could I say çeyrek saatlik here?