I understand the question is asking about whether the workplace uses テプラ or ネームランド cameras, but what exactly does the 「でしたか」 mean in this circumstance?
I looked up Tepra (テプラ) on google images and its a handheld machine makes something like nameplates on the go. Please correct if I am wrong!
Anyway, this usage of でしたか is as straight-forward as it gets: past tense of です + question particle か. Listing consecutive items using か gives a " [this] or [that]" list, like in your example.
あなたの職場はテプラでしたかネームランドでしたか
More context is definitely needed for this to fully make sense, so I had to infer as to not make a nonsensical statement.
(Did your workplace use) Tepra or Nameland (nameplate machines)?
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2In English we might say "Were you a Tepra shop or a name-brand shop?" Feb 4 '16 at 0:46
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While your interpretation sounds correct I have never seen this usage before. I wonder if it's very formal or no longer in popular use. Typically I would expect something like "XかY”. It makes more sense to me if this is really two sentences, where a period is after the first でしたか。I have also seen それとも used in a similar structure after the first option. Feb 4 '16 at 1:16
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