Original:
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下世話ですか?
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Improved:
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一般的な言葉ですか?(いっぱんてきなことばですか?)
or
一般的な表現ですか?(いっぱんてきなひょうげんですか?)
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Hello Holly-san,
Don't worry about your Japanese! I can understand what you're trying to say!
As Yusaku-san said, 強情を知る is not a common phrase and cannot be found in dictionaries and on the Internet. 強情を張る, which could be translated as "to insist/be obstinate/be stubborn," is a common phrase and can found both in dictionaries and on the Internet. However, this does not necessarily mean you cannot say, 強情を知る. If it's from a song you heard, it could mean "Someone realizes that he/she himself/herself is obstinate." In Japanese, we have this phrase 恥を知る, which literally means "to know shame." 強情を知る could be a variant of this phrase.
I hope this helps a little.