督 means “supervise, direct, urge”

とく · toku

Also: coach, command, lead

On'yomi (Chinese reading)
トク

JLPT N1 · Taught in secondary school · 13 strokes

The story

An eye (目) under 叔, uncle: picture a stern uncle keeping watch over the family business. 督 is directing: a 監督 is a film director or a team's manager, and a 督促状 is the letter demanding a payment that is overdue.

Used in 監督 (kantoku, director/manager), 督促 (tokusoku, demand for payment), and 総督 (soutoku, governor-general)

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Readings from KANJIDIC2, © EDRDG, CC BY-SA.