。
She didn't go shopping yesterday, did she?
Literal
She [topic-は] yesterday shopping [for-に] did-not-go [right?-ね].
Sentence-final ね turns a flat statement into a confirmation-seeker — it's softer than asking outright with か, since the speaker projects an answer they expect the listener to share. 買い物に行く ('go shopping') uses the purposive に: a verb-stem-based noun (買い物 'the buying') combined with a motion verb (行く), a hugely productive frame in Japanese — 食事に行く, 散歩に行く, 釣りに行く. Note that the sentence is syntactically a statement (a 平叙文), not a question, even though pragmatically it invites a response.