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Stroke order matters in Chinese: it keeps the character balanced, and it is how dictionaries and handwriting input methods expect a character to be written.
牧 is an ideographic compound. A hand 攵 leading an ox 牛.
Radical: 牛 + 4 more strokes
mù牧

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Open the tool →牧 (mù) means “To herd or pasture livestock” in Chinese.
牧 is pronounced mù in Mandarin Chinese.
牧 has 8 strokes.
牧 is written in 8 strokes, starting from the radical 牛. See the animated stroke order on this page.
The radical of 牧 is 牛, and 牧 is an ideographic compound.