I studied at this place （where I spent three years）
= I studied at this place （at which I spent three years）
括号部分是定语从句.
句子可以分为两部分：I studied at this place ；I spent three years at this place.
只不过后面一个句子在此处是以定语从句的身份出现的.
你们老师说得容易混淆在于两个句子有共同点“at this place”,当后者以从句身份出现时,由引导词 at which（=where ）引导,而这里前面已经有了at this place,因此易混淆.
希望帮到你!