。
She tucked the box under her arm and carried it.
Literal
She [topic-は] that box [object-を] underarm [in-に] hugging [then-て] carried.
小脇に抱える ('hold under one's arm') is the standard set phrase for tucking something between the upper arm and ribs to carry it — bags, books, packages. 小脇 literally means 'small armpit,' the hollow area beneath the upper arm. 抱える ('to hold in one's arms, bear, carry') covers anything you cradle or hold close — distinct from 持つ ('hold in the hand') or 担ぐ ('shoulder, hoist'). The te-form here chains tucking and carrying into one fluid action.