。
She blew out all the candles on the birthday cake.
Literal
She [topic-は] birthday-cake [genitive-の] top [genitive-の] candles [object-を] all blow-extinguished.
吹き消す is a compound verb 吹く ('blow') + 消す ('extinguish'), giving 'blow out (a flame)' as a single concept. Compound verbs of this manner+result kind are dense throughout Japanese — 焼き切る ('burn through'), 飛び降りる ('jump down'), 持ち帰る ('take home'). みな is a slightly literary or older variant of みんな ('all, everyone'); both are used as adverbial quantifiers ('all of them') and the choice carries register. Birthday cake culture in Japan is itself a relatively recent (20th-century) Western import, but blowing out candles has become as universal there as anywhere else.