The correct option is B Thanking you
Blank 7 is the closing in a formal letter. After writing the conclusion of the letter, the writers closes it, using an appropriate closing salutation.
Option B: 'Thanking you/Thank you' is a common closing as it is widely accepted in most formal letters that make a request. Hence, B is the correct option.
Option A: The term 'thankfully' does not qualify as a closing. It's an adverb of manner which does not function as a close. Hence, A is incorrect.
Option C: 'Gratefully' is generally used in 'thank you' letters and it's written as 'gratefully yours'. As this salutation is generally used as an acknowledgement of thanks, it isn't relevant here, as the given letter is an application. Hence, C is incorrect.
Option D: 'Greatly' is not a salutation and hence, D is incorrect.