Update values in one table based on contents of another
Looks like this should do it for Oracle:

UPDATE Products 
SET Products.Unit_In_Stock = Products.Unit_In_Stock - 
(
    SELECT Order_Details.Quantity
    FROM Orders 
        INNER JOIN Order_Details 
        ON Orders.Order_ID = Order_Details.Order_ID
    WHERE Products.Product_ID = Order_Details.Product_ID 
    AND (Orders.Shipped_Date IS NOT NULL) 
    AND (Orders.This_Order_Was_Shipped = "YES")
)
WHERE EXISTS
(
    SELECT Order_Details.Quantity
    FROM Orders 
        INNER JOIN Order_Details 
        ON Orders.Order_ID = Order_Details.Order_ID
    WHERE Products.Product_ID = Order_Details.Product_ID 
    AND (Orders.Shipped_Date IS NOT NULL) 
    AND (Orders.This_Order_Was_Shipped = "YES")
);