If you are on SQL Server 2012 or above, you can use LAG function to get the previous record value.
declare @Part_TBL TABLE
(YR_MTH INT NOT NULL
, Total_Part INT NOT NULL
);
INSERT INTO @Part_TBL(YR_MTH,Total_Part)
VALUES(201605,3)
,(201606,5)
,(201607,10)
SELECT
YR_MTH
,Total_Part
,ISNULL(
Total_Part - LAG(Total_Part,1,NULL) OVER(ORDER BY YR_MTH ASC)
,0) AS Different
,LAG(Total_Part,1,NULL) OVER(ORDER BY YR_MTH ASC) AS Total_Part_Prev
FROM
@Part_TBL AS S