The original sentence for the question “Which canvas appears to have been painted with a red paint?” is “This/That canvas appears to have been painted with a red paint”, and the answer would be “This one/canvas” or “that one/canvas”.
The reason why that sentence has no
does is that it is the subject noun phrase (NP) that is being questioned. When, say, an object is substituted by a wh-NP, then that
does (or anything like
must, etc.) stands between the wh-NP and the subject NP, e.g.:
“He reads The New York Times every morning.” – “The New York Times” is the object, if we put a question to it, we get:
does he read every morning?” –
does stands between the object “what” and the subject “he”.
But in the case of your canvas sentence when the wh-NP and the subject NP are the same, no
did is “extracted”1 from the predicate verb, and the verb remains as it is in the original declarative sentence. One more example:
“My father likes coffee.” – “My father” is the subject NP. By asking “whose?” we put a question to the subject NP, so no
does is extracted, “likes” remains as it is:
“Whose father likes coffee?” – direct word order.
In short, when the question is put to the subject noun phrase, the word order remains direct, like in the original declarative sentence, no
did is added to the sentence, and only what's questioned is substituted for a wh-whord.
did “extraction” I mean the transformation of the synthetic verb forms into analytic ones, e.g.: come → do come, comes → does come, came → did come.