First you will need to know how to delete records with use of SQL only. I'm guessing you allready achieved this.
Regarding the check boxes you can generate checkboxes with php linked to the id in the database. When you post your form then you can delete the records where the id's match.
In your form you submit the form with checkboxes the id's 3,5,7
On the process page you make the the querry look like the following
DELETE FROM tbl_name
How you build this querry using PHP is up to you that's the challange
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