How do I think about recursion

I got the idea for problems like factorials or finding sum from 1 to n, where there’s a pattern visible. Like this:


I got it for things like addition, subtraction, division, multiplication of two numbers as well.

eg: a+b



Now, I am wondering how it’ll be for finding a palindrome of a number? I’ve a solution but I’m not understanding how we came towards it. I’m looking for how to come towards a solution than a solution itself.