Are you saying you want to return the average price of each item in the latest month when the item was purchased? If so try this:
SELECT Items.ItemID, ItemName, FORMAT(AdditionDate,"mmmm yyyy") AS LatestMonthPurchased,
AVG(Price) As AveragePrice
FROM AdditionPermissions as AP1 INNER JOIN Items
ON AP1.ItemID = Items.ItemID
WHERE FORMAT(AdditionDate,"yyyymm") =
(SELECT MAX(FORMAT(AdditionDate,"yyyymm"))
FROM AdditionPermissions as AP2
WHERE AP2.ItemID = AP1.ItemID)
GROUP BY Items.ItemID, ItemName, FORMAT(AdditionDate,"mmmm yyyy");
The outer query is restricted by the subquery, which is correlated on ItemID, to the MAX (latest) year/month when the item was purchased, and consequently returns the average price paid in that year/month.