The correct option is B playing billiards
A comparison is being made between two activities, 'swimming' is mentioned whereas the second activity isn't mentioned but the following noun 'billiards' is mentioned. We know that billiards is a game and it would be played, so we need to change the underlined noun by adding 'playing' which is in the same grammatical structure as 'swimming' both being gerunds. Option C is hence correct and option D isn't. Options A and B do not contain the required gerund and do not complete the meaning of the sentence, hence they're incorrect.