Question

定语从句问题。they tried to think of a plan (by which ) they could fulfil their task ahead of time

为什么不用that

Answer 1

他们试图想出一个能够提前完成任务的计划。
by是介词，关系代词紧跟在介词之后时，不能用that，指物时只能用which，指人时只能用whom。而且不能省略。
但如果介词移到后面，则可以用that。而且，由于介词后面的成分叫宾语，关系代词作宾语时，只要不是紧跟在介词之后就可以省略。

上例可以说成：
They tried to think of a plan which/that they could fulfil their task by ahead of time.
或They tried to think of a plan they could fulfil their task by ahead of time.

Answer 2

他们试图想出一个能够提前完成任务的计划。