In English I think we might be more likely to say "two popular social media sites" or "popular media services"
Ok. Added as an acceptable answer :)
Actually the correct term for websites like FB and T is "social network"
Wow, what a clever comment!!!
How come the singular δημοφιλη is used?
It's not singular in this sentence but neuter plural.
See e.g. https://en.wiktionary.org/wiki/%CE%B4%CE%B7%CE%BC%CE%BF%CF%86%CE%B9%CE%BB%CE%AE%CF%82
In North America we would most likely say "two popular social networks or social media networks".
I'm glad that proper English was put in as acceptable answers but i was just presented an option where proper English was not possible as an answer. Perhaps the primary correct solution needs to be updated.
Are names of websites like this never transliterated into Greek? Even if someone were writing this sentence by hand?
They can be transliterated. It is just the personal preference of the writer to write them in Latin or Greek script.
Would one write "φεσμπουκ" and "τουιτερ"?
I like your possible Greek transliterations for FB and Twitter. I would probably add an ι between the ε and σ
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