Do you know his difficulty he had ____ his family?

选B

你知道他在支撑他的家庭遇到的难题吗？

have difficulty in doing sth. 这里省略了介词in

这句话是过去进行时
所以用现在分词

这个英语表达不地道。估计中国老师出的

have difficulty（ in ）doing sth。固定句型