Translation:There are many advertisements in the newspaper.
They're both common, but slightly different. "Reklame" covers the straight up product and service ads in the newspapers, but also TV and radio commercials. It functions like "advertisement" in that it can be used both as a category and to refer to a single advertisement.
"Annonse" is limited to newspapers and internet media; (mostly still) pictures and print. On the internet the lines get a little blurry, as "annonser" can be animated, but traditionally the distinction was clear.
However it was meant, the answer with the (at present) many ‘likes’ sounds aggressive and demeaning, in contrast to the other, helpful answers. So my thanks to CroverAzureus, KirkEasterson and CJ.Dennis, and I’d be happy if all those people who ‘liked’ the former answer would rethink their values.
(In general, though, DuoLingo is a positive experience, and I’d like to take this chance to thank not only the moderators (the Norwegian course moderator team rocks!) but especially also the simple users for all the positive and insightful support found on the discussion pages.)