Luke is able to read the letter because he spends all his time inside reading books.
Luke is not allowed to leave the house, because he is not supposed to exist. He spends most of his time in isolation, trapped in the house watching the mansions being built across the street. When the letter from the government arrives, no one in the family can make heads or tails of it—but Luke can.
Luke read the letter at supper, after everyone else in the family had taken a stab trying to figure out at what it meant. Someone, after reading all the big books that Jen had loaned him, he didn’t find the fancy words so daunting. (ch 21, p. 100)
Luke explains that the government realizes they have been buying materials to grow plants indoors, and since that is often associated with illegal activity they are being asked to stop immediately and return all of the materials to the government.
Jen is Luke’s secret friend. She is also a shadow child, but she is better educated because her parents are better at working the system. This second letter from the government (the first one told them they could not keep pigs) isolates the family even more and further inhibits them from earning a livelihood.