Question

He told me （that） he had two sons and that they both had gone to college.

Answer 1

He told me （that) he had two sons and that they both had gone to college.
意思是：
他告诉我说， 他有两个儿子， 他们都上大学了。

Answer 2

从句作直接宾语时that不能省略
that引导宾语从句时，一般是可以进行省略的。但当that引导的宾语从句充当介词的宾语时，that不可以省略。例如：I doubt (that) he graduated from Oxford. The reason lies in that she works harder than the others do.
除此之外，that引导宾语从句还有两种情况不能省略：1. 当that 从句与另一名词性从句并列作宾语时，第二个that不能省：Everyone knew what happened and that she was worried.
2.用it做形式宾语的宾语从句。I think it cool that Sam swims in the winter.