You will encounter a lot of NPCs and characters in need of your help as you venture through The Legend of Zelda: Tears of the Kingdom. Some are in a pretty serious situation, while others are in a little bit of a sillier place.
When you encounter the Hornist in the northwestern part of the map, you will quickly realize that this is one of the latter situations. While he is stuck in a hole, his demeanor and attitude is something that you won't be able to do anything but laugh at. Once you've done that, however, it's up to you to help him get out and that is a pretty easy thing to do.
Start The Hornist's Dramatic Escape
You can find the Hornist just west of Hyrule Ridge, and south of Tabantha Frontier. You will likely come across him if you follow the path to get to the Rito and cross the bridge across the large canyon that runs along this area. Eventually, you will come across the hole he is stuck in on your right, and you will see him standing at the bottom among a bunch of pieces of his wagon and more. Hop down into the hole and talk to him to start this quest.
Complete The Hornist's Dramatic Escape
You will notice a ton of parts next to you that you can use to build him his escape, including flamethrowers, balloons, and more. You can start with the balloons, of which there are two, and you can pick these up with Ultrahand to then attach to the wagon nearby. The wagon has two poles sticking up on its sides to attack the balloons to these poles.
Next, take the flamethrowers and place them inside the little baskets of the balloons. This is all you really need, even though there are more parts that you could use. In true Tears of the Kingdom and Breath of the Wild fashion, there are lot of different ways you could solve this puzzle.
Talk to the Hornist and tell him to get in the wagon, which he will do. Once he is seated in the wagon, climb up out of the hole and use a bow to take aim at one of the flamethrowers. Shooting it with an arrow will trigger both flamethrowers to shoot on and being lifting the wagon with the balloons. The Hornist will probably complain about something but ignore him and wait for the wagon to reach a level height with you.
You might be wondering how to stop him, as at this rate, he is just going to upwards and then plummet once the battery runs out. This can be stopped by grabbing the wagon with Ultrahand and quickly bringing the wagon onto the ground beside the hole. This will prompt him to get out of the wagon and thank you for your help.
For your reward, he will give you some Courser Bee Honey, as well as now appear at the Snowfield Stable, where you can complete another side quest with him.