DO you know where ______(take) the picture of the hill?

疑问词+不定式作宾语。
应该是 to take
类似的句子还有 Do you know where to go?
Do you know how to do it?等

to take.这是一道考察疑问词+动词不定式连用的题目。这种结构在句子中做主语、表语或宾语。