I assume you know how to set up a database and read/write data from and to it.
This is no easy task. First of all you need to think about how to set up your database. Will you have a table called Question with a detail relation to a table called Comment? Both your Question and your Comment table will need a relation with User. Both need to be aware of the User that created it.
Now in your page you would need to fetch the Question (you probably have a portion of the questions shown on a page and when a user clicks it you know its ID) and every detail Comment. If you are using an ORM such as Entity Framework this will be done for you almost automatically. You just have to show them.
Now for your question you will have to check if the user that is currently viewing the page is the owner of that Question (you did store the UserID in your Question table, right?). If the current viewer is the owner it sees the "Answer question myself" button. You'd have to set this in your code. You could also give the user the ability to edit his own question or comments.
I am not going to show you code since one could write an entire article about this.
And in fact, people have written articles about it.
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I hope I've given you enough idea's about how to finish your assignment. The implementation is up to you.
For further questions I suggest you speak to your teacher.