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, which usually means on'yomi readings from the kanji. You didn't learn 知's on'yomi when you learned the kanji, so here's a mnemonic to help you:
You need someone's consent before you give them cheese (ち). Cheese has the power to enrapture a person and leave them in a state of total ecstasy, so you better make sure they consent and know what's about to happen before you feed them any cheese.
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.