From 話 (hanashi, "talk," "conversation") + を + 付ける (tsukeru, "settle", "bring to terms").
話(はなし)を付(つ)ける • (hanashi o tsukeru) ichidan (stem 話(はなし)を付(つ)け (hanashi o tsuke), past 話(はなし)を付(つ)けた (hanashi o tsuketa))