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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.
冠 is an ideographic compound. A man 元 puts on a cap 冖 with his hand 寸.
Radical: 冖 + 7 more strokes
guān冠
guàn冠

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Open the tool →冠 (guān) means “Hat” in Chinese.
冠 has 2 pronunciations: guān, guàn.
冠 has 9 strokes.
冠 is written in 9 strokes, starting from the radical 冖. See the animated stroke order on this page.
The radical of 冠 is 冖, and 冠 is an ideographic compound.