"Big Buizel, Little Buizel" is one of the most frustrating requests in Pokemon Legends: Arceus, mostly because of how simple it seems yet how tedious it can actually be. It doesn't help that it's one of the earliest requests in the game.
Dorian, a red-robed guardsman, asks the player for a Buizel taller than his. What makes it complicated is that he doesn't say exactly how tall his Buizel is. Plus, it's difficult to pinpoint an oversized one on sight. Here's what you need to do to complete the "Big Buizel, Little Buizel" request.
The "Big Buizel, Little Buizel" quest should appear early in the game, right after you pass the test to join the Survey Corps. Just look for the little quest marker above Dorian's head.
Each Pokémon has a different height and weight recorded in its summary. That being said, it's inconveniently difficult to know a "big" Buizel when you see it. What might seem like an average-sized Buizel might actually be larger than average if you don't have a small one for comparison. So just keep catching Buizel until you have one that's 2'8" or taller. You can check a Pokemon's height and weight on the first page of their summary.
One Redditor reported that a 2'7" Buizel worked for them after hours of infernal grinding, though it's unclear what allowed the game to accept this over a 2'8" one. The popular guess is that the game secretly has a metric value that Imperial measurement countries can't see in the localization.
So, if you really can't find a 2'8" one, try submitting 2'7" tall Buizels. If none of them work, then it's back to the fields.
Alternatively, as reported by Kotaku, players might consider waiting until after the Kleavor boss fight. Alpha Pokemon, including Buizels, have a better chance of spawning after defeating that first Noble Pokemon. This checks out, considering I caught an alpha Bidoof and alpha Buizel after the fact.