"... it was an accident. Ariana couldn't control it. But my mother was killed."
-- Aberforth Dumbledore (DH28)
Ariana Dumbledore’s out-of-control magic accidentally killed Kendra Dumbledore during “one of [Ariana’s] rages,” when Ariana was only fourteen. (DH28) This happened right after Albus Dumbledore graduated from Hogwarts, and led to Albus becoming Ariana’s primary caretaker, in lieu of his plans to do a world tour with Elphias Doge. (DH2)
Timeline Notes
We know that this happened right after Albus graduated from Hogwarts, (DH2) and still allowed for two months of Grindelwald and Albus's relationship afterwards (DH35) before the school year started on September 1st (DH28). Therefore, it was definitely in June of that year, and probably late June given the school year was done.