Our server doesn't mind where I put ``s in this line
$query = "SELECT * FROM `cms` WHERE pnumber = 59 ";

Your host does seem a bit mad, Bruce, but it seems to be forgiving in other ways. As I said above:
Line 24 of delete.php should be:
echo "<a href='delete_record.php?pnumber=",$row['pnumber'],"'>";
The one you uploaded said:
echo "<a href='delete_record?pnumber=",$row['pnumber'],"'>";
Which works fine on your server, although God knows why!