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She picked out shoes that go with the dress.
Literal
She [topic-は] that dress [match-with-に合う] shoes [object-を] picked-out.
~に合う ('to suit / match / go with') uses に for what something is being matched against. Compare に合わせる (transitive 'make match') with に合う (intransitive 'be matching'): the transitive frames a coordinator actively pairing things, while the intransitive describes the match as a state one item has toward another — here, a quality the shoes possess toward the dress. 選び出す is a compound verb pairing 選ぶ ('choose') with 出す ('bring out'), giving 'pick out, single out from a group' — distinct from plain 選ぶ in carrying the nuance of selection from many.