This page offers a guide on how to complete Request 28: Measuring Your Compatibility in Pokémon Legends: ARCEUS (PLA).
This quest can be picked up from Belamy, who’s found near the pastures in Jubilife Village. He will ask you to show him a Pokémon that you have a high friendship with.
How to Get High Friendship with Pokémon in ARCEUS
If you’ve still got your Starter Pokémon in your team then it’s a safe bet choosing to show Belamy that one. If not, then any Pokémon you’ve had in your team for a fairly long time will suffice.
To increase friendship, you’ll need to do fairly basic things like win battles with that Pokémon and make sure they don’t faint. You can also use items to increase friendship.
After showing Belamy your BFF Pokémon, you’ll unlock the ability to show him other Pokémon so he can assess your friendship. This is useful for particular Pokémon who evolve from having higher friendships (like Buneary). You’ll also be rewarded x1 Rare Candy.