This page of the Far Cry 6 game guide contains a walkthrough of operation Room Service, one of the main missions available in El Este. The walkthrough describes, among other things, how to reach the Grand Hotel Caballero, identify and kill the Dentist, and get rid of enemies from the hotel.
Reach the Grand Hotel Caballero
This is one of the new main missions that unlock after completing an operation called New Revolution. To start the quest, you have to meet with Yelena Morales in the rebel hideout in the town of Concepcion in El Este.
The hotel is located on a hill to the west of Concepcion. If you want to increase your chances of successfully infiltrating it, then instead of going the curvy main road to the hotel, climb the hillside.
Stop the interrogation
Stealth in a hotel occupied by enemy forces can help you eliminate The Dentist more easily. For example, you can use a climbing kit on several hooks to get to the hotel roof or one of the rooms on the top floor.
The interrogation takes place in the central part of the hotel, in a partially emptied swimming pool. The easiest way to interrupt them is to shoot the Dentist in the head with a rifle or other good ranged weapon.
Leave no witnesses
The good news is that you don't have to rush to save the rebel tortured by the Dentist. You can focus on quietly eliminating the enemies in the hotel, and if you don't want to risk close-ranged fights, then stay on the rooftops or in the room on the upper floor (watch the surrounding ladders and stairs, though - enemies may try to get to you).
Getting rid of all the enemies from the hotel will play a cutscene ending this operation.