When I was fourteen, I lost my father to a subarachnoid hemorrhage.

Literal

I [topic-は] 14-years [at-のとき], father [object-を] subarachnoid-hemorrhage [with-で] lost.

A personal-history sentence. 亡くす ('to lose (a loved one)') is the euphemistic verb for having a family member die — more polite than 死なせる or 殺す. Takes the deceased person as the direct object (を). The cause is marked with で — the instrumental/causal particle indicating how the death occurred. くも膜下出血 ('subarachnoid hemorrhage') is the full medical term — a specialized compound: くも膜 (arachnoid membrane) + 下 (under) + 出血 (bleeding). Even highly educated native speakers may not spell all the kanji right, but they'll recognize the condition.