the syntax $_POST['Delete_x'] is used because the submit button on your page is an image input type:
<input type="image" name="Delete" id="Delete" value="Delete" alt="Delete" src="../../WA_DataAssist/images/Nautica/Ultramodern_delete.gif" /
An image input type does not have a value attribute. the only value posted by an image input type is the x and y coordinates of where it was clicked.
For a learning exercise, add the following code at line 1 of your delete page:
if (isset($_POST["Delete_x"])) // Trigger
this will write the entire contents of the POST array to the past when the form is posted.