The correct answer is C. After two such nights, he must be so tired as to be able to sleep anywhere.
Step-by-step explanation:
The sentence "After two such nights must be so tired as to be able to sleep anywhere" is a fragment because this sentence contains a predicate "must be so tired..." but does not contain a subject, which is an essential element in a complete sentence. In this context, to correct this sentence and make it a complete sentence it is necessary to add a subject such as "he". This correction is shown by option C that specifies who is the agent of the action.