Meaning of kěn:
kěn
肯
Verb
to agree; to consent; to be willing to; old variant of 肯[ken3]
Tā zhōngyú kěn bāng wǒ le.
他终于肯帮我了。
He finally agreed to help me.
Tā kěn bāngzhù biérén.
他kěn帮助别人。
He is willing to help others.
Tā zhōngyú kěn chéngrèn cuòwù le.
他终于肯承认错误了。
He finally admitted his mistake.