Alcohol poisoning
He hung himself and his boyfriend (Mafuyu) was the one to find his body after.
http://www.mangago.zone/read-manga/given/mf/v01/c001/2/
See the overturned chair nearby? That's when he found Yuuki hanging =(
It shows the rope too. Sad.
*Spoiler* Yuuki had a fight with Mafuyu where he tells him to die for him, he drinks himself drunk, takes the words seriously and then hangs himself
how did poor yuuki die? was it mentioned bc i dont remember