Section 4.5

So I have been working on section 4.5 since 11am this morning. I just now decided to take a break and see if anyone could help me out. I understand the traditional square of opposition and the fallacies, but I am having an extremely difficult time understanding the proving validity part. I went through and did the problems in I, II, III, and IV, but I just do not get the last part. Did anyone understand it that is willing to help me?