Well, that is simply something that you need to learn (and to remember). On slide 44 of the omega-automata chapter, the boolean operations on omega-automata are described, slides 50 and 51 describe how boolean operations on the acceptance conditions can be performed (if at all), and slides 60 and 61 discuss which automata can be expressed in terms of weaker ones.
On slide 60, you find the formula that is used in the solution to express Fb as a deterministic FG-automaton.
Maybe these slides are a recommendation for a cheat sheet.
