She was holding a white book under her arm.

Literal

She [topic-は] white book [object-を] [under one's arm-脇に] was-holding.

脇に抱える is a stock verb phrase: 'hold (something) under the arm,' literally 'hold at the side.' 抱える ('cradle, hold tightly') is for things held against the body. The に here marks the location of the holding — at the side.