Translation:These are windows, and those are chairs.
Be aware that "hanem" always implies a stronger contradiction. This sample above would go quite wild with "hanem" and they need different references: Nem ezek ablakok, hanem azok székek is quite bizarre and its meaning "not these are windows but those are chairs" as if the addressed person won't know the difference between windows and chairs. Also in this structure with hanem we will know something sure about only one set of items (the chairs). With pedig we will know for sure what set of items are windows and what set of items are chairs.
the duolingo lessons use hanem so extensively at the beginning one gets the mistaken impression is has a more general use than it does. it seemed at first to be a version of 'but' or 'on the other hand'. however it's very specific, has a very clear but limited utility and hasn't an exact equivalent in English. i was wiping out all over the place when i first tried using it in my lessons with a live teacher.
To be a bit clearer on the rules, pedig is a contrasting conjunction, and can translate as "and" or "but", whatever seems more appropriate. It works as a postposition and is placed after the topic (usually the first item) of the second clause. (Also be aware that there's another pedig that is placed as the first item in the clause (like a traditional conjunction) and means "although".)
Hanem is a replacing conjunction. It is used when the statement in the main clause is negated and the statement of the dependent clause is true instead. A good translation is "but instead". It is used at the beginning of the dependent clause, like a traditional conjunction.
I'm not sure if I would accept that... If I'm not mistaken, "however" pretty much implies opposition. As if there were some kind of conflict between the statements listed. Now, "pedig", positioned after the basis of contrasting, doesn't imply anything like that. You could just make a bullet list of similar "assignments" ("My sister is a lawyer, my husband is an engineer, my father is a mathematician and my mother is a teacher"), and it would be natural for the last one to have "pedig". It doesn't imply, by any means, that the last entry is particularly contrasted with the rest, it's just a more "elegant" way to finish the list.