Displaying only the most recent activity of an item
Try this:

    SELECT a.MaxOfShipID,
           a.Serial_number,
           a.[Recent Date],
           a.[Send_Recieve]
    FROM &lt;tablename&gt; a
    INNER JOIN 
    (
    SELECT serial_number,
           MAX([Recent Date]) AS [Recent Date]
    FROM &lt;tablename&gt;
    GROUP BY serial_number
    ) b
         ON a.serial_number = b.serial_number
         AND a.[Recent Date] = b.[Recent Date]


Update:

In your specific case:

SELECT a.MaxOfShipID,
           a.Serial_number,
           a.[Recent Date],
           a.[Send_Recieve]
    FROM tblSend_Recieve a
    INNER JOIN 
    (
    SELECT serial_number,
           MAX([Recent Date]) AS [Recent Date]
    FROM tblSend_Recieve
    GROUP BY serial_number
    ) b
         ON a.serial_number = b.serial_number
         AND a.[Recent Date] = b.[Recent Date]