public static void DeleteGeodatabase( 
   MobileGeodatabaseConnectionPath mobileGeodatabaseConnectionPath
)

{
  await QueuedTask.Run(() =>
  {
    // Create a MobileGeodatabaseConnectionPath with the name of the mobile geodatabase you wish to delete
    MobileGeodatabaseConnectionPath mobileGeodatabaseConnectionPath =
      new MobileGeodatabaseConnectionPath(new Uri(@"C:\Path-To-Mobile-Geodatabase\YourName.geodatabase"));

    // Delete the mobile geodatabase
    SchemaBuilder.DeleteGeodatabase(mobileGeodatabaseConnectionPath);
  });
}