The correct option is B engaged
Option A: 'Engaged' means 'to be busy or occupied with something'. It completes the meaning of the sentence: Most of the youngsters today are busy with social networking in all of their free time. This sentence is factual, as youngsters, as well as adults, make themselves busy with social media during their spare time.
Hence option A is correct.
Option B: 'Employed' means 'working for a pay or sum of money in return'. 'Employed' also means 'to be occupied', but it does not relate to the given sentence, because 'employed' is used in work-related sense, whereas 'engaged' means 'busy with any thing'.
Hence option B is incorrect.
Option C: 'Tired' means 'worn out and in need of rest'.
Option D: 'Implicated' means 'to bear responsibility of'.
These words do not complete the sentence in meaning, hence options C and D are incorrect.