。
She answered while shedding tears.
Literal
She [topic-は] tears [object-を] shedding [while-ながら] answered.
~ながら marks two simultaneous actions by the same subject: crying and answering. 涙を流す (なみだをながす, 'to shed tears') is a set expression — more literary than 泣く ('to cry'). The polite ました keeps the tone gentle.