Final answer:
The book 'Refugee' does not detail Mahmoud's family's destination, but context suggests they may seek sanctuary in countries like Germany, Sweden, Britain, France, or the United States.
Step-by-step explanation:
The book Refugee does not specifically mention a character named Mahmoud's family, so it is unclear which country his family is trying to escape to. However, based on the context provided, which speaks to the broader situation of refugees, many families from the Middle East, Africa, and Asia have been trying to escape to safer and more developed countries. These often include Germany, Sweden, Britain, France, and the United States. Given the reference to a flood of refugees from places like Iraq and Syria seeking to reach Europe or the US, a family like Mahmoud's might be trying to reach one of these destinations.