The correct option is
B eating
The word 'after' is a preposition here. When prepositions are followed by verb forms, the verb forms must end in -ing.
For example, 'She organizes her work by creating to-do lists.'
The same applies to the given sentence. The correct option must be a verb + ing form.
Option B: 'Eating' is a gerund that describes the action 'to eat'. It is most suitable for the given sentence, for reasons mentioned above. Hence option B is correct.
Option A: 'Eat' is a base verb and needs to be modified (with the help of preposition 'to', or it's used as a simple present tense verb) to be used in a sentence. It does not follow prepositions like 'after', hence A is incorrect.
Option C: 'To eat' is an infinitive and cannot follow another preposition ('to' is already a preposition). Hence C is incorrect.
Option D: 'Eaten' is a past participle and is used in present perfect tense. The tense of the given sentence is past. Hence D is incorrect.