N3
とても~ない
Not ~ at all, Cannot ~ at all
その考え方はとても理解できない。
I cannot understand that way of thinking at all.
Explanation
「とても~ない」 means 'there's no way I can...'. 「とても」 usually means 'very', but followed by a negative potential (「~ない」, 「できない」) it means that no matter how hard you try it is impossible: the difficulty, size or conditions go far beyond your ability. There is a feeling of helplessness and giving up: 「こんな量はとても食べられない」 (I can't possibly eat this much).
Mixed up with
A trap in multiple choice: 「とても」 with a negative is not 'very not...' but 'absolutely impossible'.
「とても~ない」 is a big gap in ability or conditions, out of reach. 「どうしても~ない」 is 'however I try it doesn't work', or 'I just won't do it, whatever happens'.