Consent
Know, Aware
noun, verbal noun
You consent and know everything that's going on. You consent and know about all this. You're aware of it.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
無理を承知でお願いしています。
I know it's unreasonable, but I'm still asking you.
この事件に関してはみなさまよくご承知のこととは思いますが、もう一度説明させていただきます。
I am sure you are all well aware of this incident, but let me explain again.
わしの娘がお前と結婚することは承知できん。
I can’t consent to your marrying my daughter.