Translation:I did not know that he is so modern.
'I did not know (that) he was so modern' jest również poprawne. http://english.stackexchange.com/questions/149120/i-didnt-know-you-liked-her-or-i-didnt-know-you-like-her
There's technically nothing in the original sentence to match "he". The sentence has two implied subjects: (Ja) nie wiedziałem, że (on) jest tak nowoczesny.
"Ja" is known from the form of the verb, and we know that it is "on" because firstly, "jest" points out we have 3rd person singular, and then the form of adjective "nowoczesny" precises that this 3rd person sg is masculine.
For PL->ENG version of this exercise, options with specifying the subjects (or just one of them) are of course accepted.