First find the number of rooms per floor in the first wing: 32 rooms/hall * 6 halls/floor = <<32*6=192>>192 rooms/floor
Then find the total number of rooms in the first wing by multiplying that number by the number of floors: 192 rooms/floor * 9 floors = <<192*9=1728>>1728 rooms
Then find the number of rooms per floor in the second wing: 40 rooms/hall * 9 halls/floor = <<40*9=360>>360 rooms/floor
Then find the total number of rooms in the second wing by multiplying that number by the number of floors: 360 rooms/floor * 7 floors = <<360*7=2520>>2520 rooms
Then add the total number of rooms in each wing to find the overall total: 1728 rooms + 2520 rooms = <<1728+2520=4248>>4248 rooms
#### 4248