Using decomposition of Poisson processes, the arrival of men is a Poisson process with rate 6 per hour while the arrival of women is Poisson with rate 4 per hour and the two arrivals are independent of each other.
I'm assuming that the store can accommodate an infinite amount of customers and so for the men customers, it's equivalent to an queueing system while for women, it's . All the customers are served upon entering the store and so the long-run distribution of men will not explode
Additionally, it's stated that the store has been opened for a long time and so what we need here is the equilibrium distribution. For , the equilibrium distribution is Poisson with parameter a = mean arrival rate * mean service time. For , due to the insensitivity property, the equilibrium distribution is also Poisson with the same parameter.
p/s: Ithaca? Are you from Cornell?