。
She lost her hearing in that explosion.
Literal
She [topic-は] that explosion [from-で] ears [subject-が] became-unable-to-hear.
で here marks the cause or means — explosions, accidents, illnesses, all the things that produce changes-of-state can be marked with で. 耳が聞こえる literally 'ears can hear,' and its negative-potential 聞こえない means 'ears cannot hear / [is] deaf.' Adding ~なる ('become') gives the change-of-state verb 聞こえなくなる: 'become unable to hear,' which the past form puts at a specific moment. 耳が聞こえない is a relatively neutral idiom for 'be deaf'; in formal contexts, 耳の不自由な ('ear-impaired') is the more careful term.