The reason for Gale's name being in the reaping forty-two times relates to the tesserae system.

Under normal circumstances, the year a person turns twelve, their name goes into the reaping bowl once. At thirteen, it goes in twice, and so on until they reach the age of eighteen, when their name will be automatically entered seven times.

The reason that Gale Hawthorne's name is in the bowl forty-two times rather than seven is because he has needed to enter himself more times in order to get tesserae for himself and his siblings. Having a tessera entitles a district resident to collect a year's supply of grain and oil; it can be collected by an individual for themself and for members of their family. Gale, who has been collecting tesserae for the five people in his family for seven years, has earned himself an extra thirty-five entries. These thirty-five entries, together with the seven for his age, amount to forty-two.

Another way of thinking about this is that his name is entered forty-two times because of the injustices of life in Panem. As a resident of the districts, Gale is powerless to uplift himself or transform his circumstances. The only thing standing between his family and starvation is the tesserae that he signs up for.