One way to do this is to use a left outer join:
Select Distinct E.empid, lastname, firstname
From HR.Employees as E left outer join
Sales.Orders as O
ON E.empid = O.empid and O.orderdate = Convert(datetime,'02/12/2008',101)
where o.orderdate is NULL
If there is a match between employees and orders on the date, then the where clause ignores those records.
This query is rephrasing your logic. You say "I want get all empids' who didn't not handle orders on February 12 , 2008". The way this works is it actually matches the employees to orders on that date. However, because it uses a left outer join, the match leaves a NULL when there is no match. These are the ones that you want.
In a sense, this query answers the equivalent question, phrased as "I want all empids that fail to match an order on such-and-such a date."