It doesn't mean anything! The words 'concerned' and 'of' are not connected. Try dividing the sentence up like this: Homework can be excused only after the receipt and approval (by the teacher concerned) of a letter from a parent setting out the reasons. The word 'concerned' belongs with the phrase "the teacher concerned". This means the teacher in question ( i.e. the teacher who set the homework). The word 'of' belongs with the phrase 'after the receipt and approval of a letter'. In other words, homework can only be excused after "the teacher concerned" has received and approved a letter from the parents.

Hello Morteza, There is confusion here due to a lack of punctuation. If commas are inserted appropriately, thus: Homework can be excused only after the receipt and approval, by the teacher concerned, of a letter from a parent setting out the reasons. ...and you now read this, pausing at the commas I think you will understand what I'm getting at. If there is still a problem please do let me know. Kind regards, James.