Have a separate table with at least three columns: one for the user ID, one for the question ID, and one for the checkbox ID. If user 1113 checks boxes 1, 3, and 5 of question 9; there will be three rows in the table
userID | questionID | checkboxID
-------+------------+-----------
1113 | 9 | 1
1113 | 9 | 3
1113 | 9 | 5
And there will be other rows for other users and other questions.
And there's a database forum here for database questions.