Question

Richard told his son, "(Your You're) young, but when you grow up, you'll understand.

Answer 1

Answer: you're

because you're is the contraction "you are" which makes sense in this context. "your" is a possessive and does not make sense in this context. an example if the correct usage of "your" is:

"it's your cat"

Answer 2

You're stands for 'you are,' so, if you were to say this sentence outloud, you would say:

Richard told his son, "You are (You're) young, but, when you grow up, you'll understand.

*You also use you're to describe something or someone, and, your to describe ownership, for example: Your clothes look nice. VS You're looking great today!*