Understanding, Roger
Noun and する verb
りょうかい
彼は弱々しいうなずいて了解の意を示して、立ち去った。
He expressed his understanding with a weak nod and walked away.
When you've finished solving something, you've come to a point of comprehension and understanding. Also, used in (often radio) communication to signify you know what's up. It's like saying "roger!"
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.