The given passage is in past tense, hence the underlined word 'wake' is incorrect. 'Wake' is in the simple present tense/future tense form.
Option C: 'Woke' is in the simple past tense, it's the most appropriate option. The sentence sounds complete in meaning: "After many hours of deep sleep, Gulliver woke up."
Hence option C is correct.
Option A: 'Waking' is a present participle. It is used in the present/past continuous tense. But the given sentence does not indicate an action that is continuous. It indicates an action 'to wake up' that completed in the past (simple past tense). Hence option A is incorrect.
Option B: 'Sit' is in the present tense. Also, 'sit' is generally used in the second person narrative 'you sit down'. It isn't used when the subject is in the third person, i.e. Gulliver. Hence option B is incorrect.
Option D: 'Slept' is not relevant to the given sentence, as Gulliver was already in a deep sleep. After deep sleep, one can't sleep 'up' (Gulliver... up). Hence D is incorrect.