SQL Select where value = to another select
You can use a CTE for this work:

WITH ctSum AS
(
    SELECT   customerId, SUM(PartQty) as TotalQty
    FROM     OrdersParts
    GROUP BY customerID
)
SELECT a.customerID, a.Total_number_parts
FROM   Orders a
JOIN   ctSum b
ON     b.customerID = a.customerID
WHERE  a.Total_number_parts = b.TotalQty;


Or if you prefer another syntax:

SELECT a.customerID, a.Total_number_parts
FROM   Orders a
JOIN   (SELECT   customerId, SUM(PartQty) as TotalQty
        FROM     OrdersParts
        GROUP BY customerID) b
ON     b.customerID = a.customerID
WHERE  a.Total_number_parts = b.TotalQty;