How many days does the young Scrooge get to spend with his father and sister before he has to start work?

In Stave 2 of A Christmas Carol, Scrooge is visited by the Ghost of Christmas Past. Together, they return to Scrooge's school days, specifically to a visit from his sister, Fanny. She has come to collect Scrooge for the Christmas holidays but does not state exactly how many days this will be: "We're to be together all the Christmas long, and have the merriest time in all the world."

This reference may refer to the period know as the Twelve Days of Christmas which begins on Christmas Day, December 25, and ends on Epiphany, January 6. The Victorians honoured the Twelve Days of Christmas and counted each day, until Epiphany, as part of the festive season. 

For Scrooge, the return to his family was marked by great excitement and joy but is significant as his last term at school. From January 6, he would be apprenticed to Mr. Fezziwig when his transition to adulthood (and miserliness) begins.