"Mae'r llygoden yn frown."

Translation: The mouse is brown.

[sbnaidu]

Why do we mutate brown in this case?

[rmcode]

This construction to describe things 'Mae (something) yn (description)' always mutates the adjective following 'yn'

Mae'r llygoden yn frown - The mouse is brown

Mae'r llygoden yn ddu - The mouse is black

[EllisVaughan]

yn causes noun to mutate softly, unless it mean in where it causes a nasal mutation.

[HerrArbo]

If llygoden is feminine why does it not mutate to "mae'r lygoden"?

[EllisVaughan]

Because the mutation of feminine nouns after "y" is what's called a weak soft mutation which does not affect "Rh" or "Ll".