English translation:
Not at all
Structure:
とても + Verb[ ない ]
I have problem with this particular grammar point. I am doing my reviews using path for Minna no Nihongo which I used as my main textbook. There is a grammar point in this textbook about using とても and あまり, but in this case とても is used in affirmative way and あまり with negatives. That’s why in my reviews I always want to use あまり for sentences with negatives. Is とても plus negative some advanced grammar (which should be on higher level) or is it a mistake and it should be あまり instead?
Hey 
I don’t think it is really advanced grammar. They can both be used with negative and affirmative sentences. It might simply be not covered by the book. (Though あまり always has negative nuance)
とても with ない (like まったく and 決して) completely negates sentence.
Something is absolutely impossible to do, or to happen.
While あまり + ない means not much, not very.
In other words, something exists, but qunatity, amount, degree is low.
You can easily see this by comparing those two sentences:
あまり肉を食べない。
I don’t eat very much meat. (but I eat a bit)
とても子供を叩けない。
I cannot possibly hit a child. (it is totally impossible for me, complete negation)
Thank you for your reply. Maybe it will help me to clarify which is needed during reviews 
But I admit, the existence of 全然 in this case is not helpful at all 
I think I need to go back to theory and study once more differences between these expressions.
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Should 「とっても」 be a possible answer in any of these 「とても」 related grammar points?
The more I think about it, the more it doesn’t seem to matter.
@Aythreuk Hey! While とっても and とても are normally interchangeable, with とっても generally adding more emphasis/being stronger than とても, it is better to use とても in this structure as it is closer to a set phrase (とても〜ない rather than just とても). とっても can also be considered more colloquial/spoken than とても and should be avoided in written language. That being said, we weren’t catching とっても for this grammar point, so I have updated the answers that throw hints/warnings to display the above information. Cheers!
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I had the same confusion as @Arashi as the specific page mentioned by the resources in this grammar lesson points to Minna no Nihongo I, page 56, CH8 where the basic forms of totemo and amari are shown but not totemo~nai.
I’m cramming Minna no Nihongo I as I’m restarting my language studies but I had never seen this form before. nbd though