I did a test with the example data you posted.
SELECT Sum(LastItemBal) AS SumLastItemBal FROM (SELECT DISTINCT Accounts.InternalFileNo, DLookUp("Balance","Accounts","InternalFileNo=" & [InternalFileNo] & " AND ItemNo=" & DMax("ItemNo","Accounts","InternalFileNo=" & [InternalFileNo])) AS LastItemBal
FROM Accounts) AS Q1;
That query returns a single value which is a grand total of all the last ItemNo Balance for each InternalFileNo.
This gets the same result:
SELECT Sum(Balance) AS SumLastBal FROM (SELECT * FROM Accounts WHERE AccountID IN (SELECT TOP 1 AccountID FROM Accounts AS Dupe WHERE Dupe.InternalFileNo=Accounts.InternalFileNo ORDER BY InternalFileNo, Dupe.ItemNo DESC));
Since the second query doesn't use domain aggregate functions, it is the better option.
If you want to view detail records that contribute to the Sum, then don't do the outer query. Use the remaining nested query as the data source for a report. Use report Grouping & Sorting features with aggregate calcs in footers. This will allow viewing detail info as well as summary calcs.
If you want to learn more about subqueries, start with
http://allenbrowne.com/subquery-01.html#TopN