Although I agree with the above answer, it does not insist on a particular photograph. If you really need to ask "With which camera was this particular picture taken", I would go with :
この写真{しゃしん}はどんなカメラで写{うつ}されましたか。
I will explain the main grammar point: 写す
means "to photograph". In this case, we want to ask how this picture was taken, hence, we use the passive form. Then we use the で
particle to denote the means by which the action was done. Note that if you are more familiar with 撮{と}る
as a verb, you can use it exactly in the same way:
この写真{しゃしん}はどんなカメラで撮{と}られましたか。
In fact the above sentence translates quite directly to:
With which camera was this picture taken?
The passive form is a very useful construct, I can only encourage you to read around, there are plenty of good resources online!