欢

Right radical 欠 depicts a person with mouth wide open exhaling - used for breath-related and mouth-open actions. Anchors 欢 in the image of joyful laughter, the open-mouthed exhale of delight. Same 欠 radical in 歌 (sing), 歇 (rest), 次 (next), 吹 (blow) - all activities involving an open mouth or pause for breath.

Left 又 (right hand) is a graphic placeholder in the simplified form. Traditional 歡 had the elaborate 雚 (huān, heron) phonetic on the left; the 1956 reform replaced it with 又 for simplicity - a stand-in shape that no longer carries phonetic value. Same 又 substitution appears in 鸡 (chicken) and 难 (difficult) where 又 replaces complex left-side phonetics.