It's that day, the one that comes twice a year, when Doug and Tom get to beat the you-know-what out of something.What's that thing? Rugs, silly.
Their mother, along with Grandmother and Great-grandma Spaulding, go outside to clean the rugs. Back in the day before you could rent a Rug Doctor at the supermarket, this meant you hung them over the clothesline and beat them with what Bradbury calls "wire wands."
Great-grandma says to Doug and Tom, "Get the flies, boys, kill the cooties!"
As they're doing so, they recall where the stains came from: fifteen years of their dad spilling coffee, their mother dropping the cream, the boys leaving scuff marks (not, we assume, with their magical Cream Sponge Para Litefoot sneakers, but rather with their hateful winter boots).
Tom gets all excited about the patterns in the rugs and says, "It's fun seeing things." Tom is easily entertained. He also feels he can see the future in the rugs, the stains yet to be made. Note that Bradbury is, in a sense, talking about time travel here.
Doug, though, is having an emo moment about the Happiness Machine. He was counting on Leo Auffmann to "keep things in order, keep everybody smiling."
The chapter ends with Tom giving the rugs a last good whack, stirring up "the dust of five thousand centuries."