Through the years I would guess at---I thought was the corre

如果不用连接代词,原本是这样的：
Through the years I would guess at【the answer tha/ which】I thought was the correct answer
因为这样便于下文的the correct answer 中的answer 重复了,于是便用what.
语言点：
What 引导名词性从句时相当于【先行词+ 关系代词】这句为【the answer先行词+ tha/ which关系代词】
全句意为：
这些年来,我一直在揣摩着我认为是正确的答案.