Hint:First we must read all the given options and we must know the usage of the words. Later we must know the usage of the different words. Choose the option which will be grammatically correct. Also we must see that the selected option will make the sentence meaningful.
Complete step-by-step answer:
The above given options are combinations of verbs and modal verbs.
Now let’s examine and understand the given options above.
Can’t sleep: the verb ‘can’t sleep’ is indicating present incapability but the given sentence is about past capability and ability. So this option can’t be appropriate.
Can sleep: the verb ‘can sleep’ is indicating present capacity or ability but the given sentence is about past inability. So this option can’t be appropriate.
Could sleep: the modal verb ‘could sleep’ is used as the past tense of the verb ‘can’ it indicates ability but again it is clear that the given sentence is about past inability. So this option can’t be appropriate.
Couldn’t sleep: this option(C) is absolutely appropriate because this modal verb is indicating past inability or incapacity and the given sentence is about past inability. So the correct sentence is ‘You look tired’. ‘Yes, I couldn’t sleep last night’.
Option C is the correct answer.
Note:Verb is a word that describes an action or work. Modal verb is a type of verb that expresses necessity or possibility of an event.