Hi Victor, To “hand in an assignment” means to deliver or submit an assignment (or a piece of work). The first person in this conversation is saying that handing in an assignment a month late is not allowed, or not possible. It seems like the second person’s response, then, is a little joke, because they ask for an extra week. I hope that makes it clearer for you

This is a joke. The assignment is a month late. The person accepting it - or not accepting it, really - says "you can't hand it in a month late" - this means the person handing in the assignment is too late, and the deadline has passed. The assignment will not be accepted or marked. The person trying to submit the assignment then asks for an extra week - so that the assignment will be a month and a week late. Obviously this is silly, which is what makes it (in intention) funny.

you can't turn in the assignment late, you can't submit the assignment past the due date