From the circled date until 31 December of the same year, both days included, a gurdwara serves extra langar every Tuesday. How many Tuesdays is that?

The circled 10 October 2028 is a Tuesday. Up to 31 December is 31 − 10 + 30 + 31 = 82 days later = 11 weeks + 5 days, so there are 11 more Tuesdays after it (the last on 26 December): 1 + 11 = 12. (11 forgets the circled Tuesday itself.)