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direction; way
person; lady; gentleman
method of; manner of; way of
care of ...
person in charge of ...
side (e.g. "on my mother's side")
「方」 has other readings with different meanings.
駅はどちらの方ですか。
Which direction is the station?
あの方は誰ですか、教えて。
Who is that person? Tell me.
あの方が新しい先生です。
That person is the new teacher.