You can skip the first FROM, but not the second if you are going to use a JOIN later.
In ANSI syntax, FROM is mandatory and you need to say:
DELETE FROM tbl WHERE ...
But this FROM is optional in SQL Server.
On the other hand, the ANSI syntax does not permit for the FROM clause in DELETE but you would have to write something like:
DELETE FROM Sales.SalesPersonQuotaHistory
WHERE EXISTS (SELECT *
FROM Sales.SalesPerson AS sp
WHERE Sales.SalesPersonQuotaHistory AS spqh
AND Sales.SalesPersonQuotaHistory.BusinessEntityID = sp.BusinessEntityID
AND Sales.SalesPersonQuotaHistory.date= sp.date
AND Sales.SalesPersonQuotaHistory.sourcesystem= sp.sourcesystem
AND p.SalesYTD > 2500000.00);
And, yeah, since you cannot have a FROM clause, there is no provision to define an alias for the target table of the DELETE.
But this is ANSI-compliant SQL. And most of us, don't care if we are ANSI-compliant or not.