The one path by the Kripke structure is
{a} {} {} {} …
In the first step a is true, in all other steps ¬a is true. Xa isn't true in any of them.
Hence, we find no step where ¬a & Xa holds, Thus, the first formula cannot be satisfied.
If we look at the second step, we see that both a and previous ¬a are false. Thus (previous ¬a)<->a is satisfied there. Hence, also F ((previous ¬a)<->a) is satisfied in the second step. Thus, EX(previous ¬a)<->a is satisfied in the initial (first) state of the path and thus of the Kripke structure.
