The correct option is B Kartik said that he would be studying the next day.
Direct speech is a sentence in which the actual words of the speaker are quoted.
Indirect speech is a sentence in where we report what someone said, without quoting his exact words.
In Future Continuous Tense 'will be' changes into 'would be'.
Here, option B is correct. 'Will be' changes into 'would be'. Pronoun changes accordingly. 'Tomorrow' changes into 'the next day'.
In option A verb is not changed. So, it is incorrect.
In option C pronoun is not changed. So, it is incorrect.
In option D 'that', a conjunction is not used and pronoun is wrong. So, it is incorrect.