Talking through what the expectations are, what you're thinking and what you're doing help cover points where you may make a mistake and vitally where there's a disconnect with your understanding and theirs.

I've had paper problems to do that to solve the literal problem in front of me would be to write some very short code. But the problem looks like a shrunken version of a bigger system, and so explaining this shows I'm not just over engineering this toy problem I'm showing I understand (this was an early position) classes and inheritance and how to manage that.

Are you asking how I'd build systems to do this kind of thing? Are you asking what I'd do if the boss comes over and says they need this one off thing done asap?

You want to be seen as someone they could actually work with on something.