For American residents, $0.9609/Euro, that is, the dollar in the local currency is used to measure the price of a unit euro. This is the American price tag-direct price tag (just like if they buy a KFC set meal, the price is $3/serving, and how many dollars are used to express the price of unit goods). On the contrary, 1.0407 Euro/USD becomes their indirect price, which is the European price.
Similarly, for euro zone residents, $0.9609/euro is an indirect European bid, while 1.0407/euro is a direct American bid.