。
She had a deep attachment to the old house.
Literal
She [topic-は] that old house [target-に] strong attachment [object-を] was-having.
愛着 ('attachment, fondness, sentiment') is a Sino-Japanese compound from 愛 ('love') + 着 ('attach') — feeling stuck-with-love, the warm emotional tether to a person, place, or possession. ~に愛着を持つ ('hold an attachment to') takes に for the target. The progressive ~ていた describes the sustained state at a past reference. Old houses in Japan often carry deep 愛着 — 古民家 (traditional country homes) are increasingly cherished, restored, and repurposed as the population moves toward cities.