Question

We hope the little____we've been able to do has been of some use to you.

填WHAT 还是THAT 为什么 谢谢，请讲详细些！

Answer 1

你好。答案是THAT.
把你的句子分成两句，就容易理解了。
1 we hope the little has been of some use to you.
2 we have been able to do the little.再把它们合并起来（用定语从句）：We hope the little (that / which ==the little) we have been able to do has been of some help to you .

Answer 2

what定语从句啊，句子主干是we hope something has been of some use to you.这里的something就用the little及其定语替代