"Isn't the wind strong?"
From what I understand, this is something that someone might say, but not write. In this case, the wa/ga is replaced by a verbal pause, which is indicated by the comma in the correct solution. They don't give you a comma when constructing the sentence, though, so it's kinda confusing >.<
It is just the way the i-adjectives inflect:
つよい - strong
つよく - strongly
つよくない - not strong
つよかった - was strong
つよくなかった - wasn't strong
Edit: ...And I misunderstood and did not answer your question well. Sorry about that.
The right answer is that the -い ending is the adjective form while the -くending is the adverb form (added above):
つよいかぜがふきます - A strong wind blows. かぜがつよくふきます - The wind blows strongly.
I'm pretty sure the only difference is ending with か vs ね (and as in this particular question sometimes using a comma in place of the は):
Isn't the wind strong? = 風, 強くない です か。
The wind is not strong, is it? = 風 は 強くない です ね。
And I think "Is the wind not strong?" would be the same as the first sentence.
Without any context, "Isn't the wind strong?" could also mean "The wind is strong, isn't it?" 「風は強いですね？」
It could also be "Is the wind not strong?", which to me is a less ambiguous translation of「風は強くないですか」.
"I can't fly my kite." "Isn't the wind strong?"
"My kite's tugging at the string so hard I can barely keep hold of it." "Yeah, isn't the wind strong?"
I was imagining two people walking on a bridge and one of them asked the other "isn't the wind strong?" as another way of asking "the wind is strong, isn't it?"
So I translated the sentence as 風は強くないですね and it was marked as incorrect. Is this because my answer hasn't been accepted yet, should I have said 風は強いですね, or is my sentence just wrong?
The translation for "Isn't the wing strong" would be, as duolingo teaches it, "風は強くないですか". From my understanding, ね doesn't turn the sentence into a question, it is the equivalent of using intonation to suggest you want your listeners approval. So my guess would be that か is required at the end of the sentence.