A large, extended family decided to buy all of the even numbered houses in Smith Street, so they could be neighbours. They bought the houses from 2 to 12. One set of grandparents bought the house at one end of the street while the other grandparents bought the house at the opposite end. The Lee family, with three young children, bought a house which is a multiple of three. If four is a factor of the house number bought by the Shin family and the Kim family bought the house between the Lee family and one of the sets of grandparents, what is the number of the house bought by the Ng family?