Sequential game equilibrium strategy question
I think the question has a typo. Whoever wrote it was trying to make you think about the fact that a, c and d are not even properly defined strategies for player B. This is because a strategy must specify what player B would do in all possibly scenarios he might face. 

However, the typo comes from the fact that b is not part of a NE. If the first payoff instead of being (3,5) it was (5,3) then b will be an equilibrium strategy for B. 

Your intuition is partially right, for it to be an NE strategy it had to choose the highest payoffs on the path of play. If it was a SPNE it would have to choose the highest payoffs in all subgames, not only the ones that are reached in equilibrium.