You are confused with quantification over paths and variables. The path quantifier A in AF phi asks whether for all infinite outgoing paths eventually phi holds. As the example solution explains, that is not the case since there is a path that violates this.

You believe that in s5, we can ALWAYS finally reach to {s2,s3,s6} which would be written as GF{s2,s3,s6}, and even EGF{s} but the exam problem asks for AF{s2,s3,s6}.