The correct option is C Yours,
According to the lines, you have to imagine that you're writing a letter to your friends, inviting them for dinner.
So, you need to choose a closing that is appropriate for informal letters.
Options A and B: We use these closings 'yours faithfully' and 'yours respectfully' for formal or semi-formal letters.
We do not end an informal letter with such closings. Hence options A and B are incorrect.
Option D: 'Dear friends' is an opening with which you begin a letter. The question asks for a close. A letter does not end with 'dear friends'. Hence option D is incorrect.
Option C: 'Yours' is the most suitable option, as it's used in informal letters. It's the simplest way to end an informal letter.
Hence option C is correct.