Simple: there are no matching rows.
Start with SSMS and try each part of the query. Start with just:
Select task_desp from Assign_taskk where due_date >= '6/26/216'
And see exactly what rows it returns.
Then, use those rows to check the second part as well. And then the final one.
I'm guessing that it's the date: SQL doesn't particularly like European dates, and prefers ISO: yyyy-MM-dd so it's possible that your date is just converting badly. It's also possible that you are storing dates in your DB as NVARCHAR or VARCHAR and that that is causing the problem.
We don't know - we don't have any access to your data, so we can't check. So you will have to do this one yourself!
(But I'd suspect that your database is a bit badly organised if you need two nested SELECTs just to handle the WHERE clause - I think a design that supported JOIN instead would be a lot easier to work with.)