(not) possibly; by no means; utterly
Always used with a negative predicate (ない, できない, 無理, etc.) to express strong impossibility or denial. Emphasizes that something is completely out of the question.
この問題は難しすぎて、とうてい解けない。
This problem is too difficult; I can't possibly solve it.
His proposal is utterly unacceptable.
There's no way I can believe what he's saying.
There's absolutely no way to finish this amount in one day.
I simply cannot understand why he did such a thing.