¿Cuál es la diferencia entre understand y figure out, make sense ?Puedes dar oraciones como ejemplo.

I'll use a sentence to explain the difference in nuance

I understand why she didn't come.
VS
I figured out why she didn't come.
VS
It makes sense why she didn't come.

let's say the reason is: her ex-girlfriend was there and it would be awkward.

I understand why she didn't come -> you knew that her ex was there, and it is about understanding her feelings. It gives the impression of "I understand her feelings and I'm not angry at her for not coming."

I figured out why she didn't come -> you were hung up on it ("hung up on" means to think hard, or 思い詰める) and were trying to figure it out; it was a mystery to you. But then you remembered that her ex was there. "I finally solved the mystery of why she didn't come."

It makes sense why she didn't come -> This has less of a nuance to do with having empathy for her like with "understand". It is like "rationally, I can understand."