If you want to show your agreement with someone you need to nod at them so they know.

The reading for this word is an exception. Here's a mnemonic to help you remember it:

You seem to nod your head a lot when you're at the unagi zoo (うなず). Unagi zoos are really rare and hard to get into. So while you're there, keep nodding to everyone because you're so honored to be there!

肯く also has two readings. うなずく is the standard, but うなづく is more and more acceptable these days too. Luckily they sound pretty similar (if not the same), so they should be easy to remember!