Rate law equation - orders?
You are correct, the reaction order cannot be deduced from the brutto-equation and is usually determined experimentally.

However, here you are presented with the elementary reactions and their rates. Obviously, the slowest step is the bottleneck and controls the overall kinetics, hence the total rate matches the rate of the slowest step. And as this is an elementary reaction, you just apply the law of mass action and use the stoichiometric coefficients for the rate equation.