The correct answer is: Only conclusion II follows.
The first statement is “Some men are educated.” This means that there exists at least one man who is educated. The second statement is “Educated persons prefer small families.” This means that all educated persons prefer small families.
The first conclusion is “All small families are educated.” This conclusion does not follow from the premises. The premises only say that there exists at least one man who is educated and that all educated persons prefer small families. They do not say anything about whether or not all small families are educated.
The second conclusion is “Some men prefer small families.” This conclusion does follow from the premises. The premises say that there exists at least one man who is educated and that all educated persons prefer small families. This means that there exists at least one man who prefers small families.
Therefore, the only conclusion that follows from the premises is “Some men prefer small families.”