To locate a file with a known extension but an unknown name in a large directory, we can employ a specific search strategy within File Explorer. Let's explore each of the options provided and why the first option is the correct one:

1. Using the Search box in File Explorer with *.ext
   This is the correct method. In Windows File Explorer, you can type *.ext in the search box (where .ext is the extension of the file you're looking for, e.g., *.txt for text files, *.jpg for JPEG image files). This instructs File Explorer to list all files with the specified extension within the current directory and its subdirectories. This method is efficient and user-friendly, allowing you to quickly locate files based on their extension regardless of their names.
2. Checking the Recycle Bin
   This method is incorrect for searching files based on extension in a large directory. The Recycle Bin only contains files that have been deleted, and it does not allow search based on file extension independently.
3. Using the dir command
   While the dir command in Command Prompt can list files, using it with file extensions requires additional parameters and is not as straightforward as using the File Explorer search box. It also lacks a graphical interface, making it less intuitive for users unfamiliar with command-line operations.
4. Through File Explorer
   This option is vague as it does not specify the method of using File Explorer. Simply browsing through File Explorer without using the search box is not practical for finding files with a specific extension in large directories.

Therefore, the best approach given the options is Using the Search box in File Explorer with *.ext because it is straightforward, efficient, and effective in locating files based on their extensions.