First find the total time Billy spends on laundry: 2 loads * 9 minutes/load = <<2*9=18>>18 minutes
Then find the total time Anna spends sweeping: 3 minutes/room * 10 rooms = <<3*10=30>>30 minutes
Then find how much longer Anna has already worked than Billy: 30 minutes - 18 minutes = <<30-18=12>>12 minutes
Then divide the difference in work time by the time to wash one dish to find the number of dishes Billy has to wash to work the same amount of time as Anna: 12 minutes / 2 minutes/dish = <<12/2=6>>6 dishes
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