。
She spoke to the children in a gentle voice.
Literal
She [topic-は] children [target-に] gentle voice [with-で] spoke-to.
話しかける ('to call out to, speak to, address') is a compound verb made from 話す ('to speak') + かける ('to apply, throw, hang') — the second verb adds the directional 'toward' nuance, marking the speech as directed at someone rather than just spoken in general. The recipient takes に. The で here marks the means/manner — 'with a gentle voice' — one of the many functions of で beyond location ('at') and instrument ('by means of').