Who dies and how in the most dangerous game

the correct answer is 4) infinitive phrase with a direct object

the explanation is that the infinitive phrase, "to with the younger children", functions as the object. it means the thing that the subject does.

1) no infinitive is incorrect because there is an infinitive verb in the sentence.

2) an infinitive only is incorrect because it is not in isollation. it is part of an infinitive phrase.

3) infinitive phrase with a subject is incorrect because in this example the infinitive phrase does not function as the subject doing the action of the sentence.