public static void DeleteGeodatabase( 
   FileGeodatabaseConnectionPath fileGeodatabaseConnectionPath
)

{
  await QueuedTask.Run(() =>
  {
    // Create a FileGeodatabaseConnectionPath with the name of the file geodatabase you wish to delete
    FileGeodatabaseConnectionPath fileGeodatabaseConnectionPath =
      new FileGeodatabaseConnectionPath(new Uri(@"C:\Path-To-File-Geodatabase\YourName.gdb"));

    // Delete the file geodatabase
    SchemaBuilder.DeleteGeodatabase(fileGeodatabaseConnectionPath);
  });
}