I ------（take）a taxi if I had realized that it was such a lo

would have taken
虚拟语气的用法
should have done本来应该做（实际上没有做）
You are late again. You should have taken a taxi.
could have done本来能够做某事
I could have helped you but I was really very busy then.
would have done本来会做某事,本来可能做某事
I would have taken a taxi if I had realized that it was such a long way.
如果当时我意识到有这么长的路程,我肯定会打的来的.

would have taken 本可以做却没做

由if I had realized that 可知此句为虚拟语气，虚拟语气中从句用过去完成式，主句要用一般过去式

would have taken虚拟语气
从句用过去完成时had realized
主句用would have taken