Solution:While all the options seem reasonable; you have to choose the one that reflects the qualities of a citizen-centric civil servant.Option (a) is not appropriate; because waiting for 2 hours again for him will not be possible. He is from a far off village and has already waited enough. This would give a wrong signal about the administration and put the villager's morale down.
Option (b) will not be appropriate because a junior officer may not be placed well enough to handle the powerful landlord's issue. Moreover, he has come so far to see you and speak to you about his problem. You should not do file and application pushing with him.
Option (c) is more appropriate because a senior subordinate officer will be better placed to deal with his problem. Moreover, you are personally calling the officer and giving him the application. This will show the villager that you are taking the matter seriously.
Option (d) is less preferable because the villager will not have time to discuss his problem. And it may give him an impression that you are not taking the matter seriously. Still it is better than (a) and (b).