Wow...
I don't know if you can comprehend. He wants to ask him what happen but he doesn't know if he wants the answer.
i actually think was legit asking cuz he wants to know more about Haesoo's heartbreak. Haesoo is Taku's subject of study for his art but Taku is now feeling a little conflicted cuz he is starting to have feelings for Haesoo. Taku knows what happened. He wants to know the details of how it happened, what was said, etc
It's up to me how I comprehend things. I'm not obligated to comprehend thinks like you do.
*things
Takyung: I want to ask what happened but I don't know if I should.
Me: Dude that's technically 'asking ' .