とても～ない

とても～ない means "can't possibly", "there's no way": the task is far beyond what you can manage. とても comes before a negative verb, usually a potential – たべられない食べられない, できない, しんじられない信じられない – often with the obstacle stated first.

とてもむり無理だ, "completely impossible", works the same way, since むり無理 already carries the negative.

"Very" or "can't possibly"

In a positive sentence とても means "very": とてもおいしい. Before a negative verb it becomes "can't possibly", and that is this pattern. Before a negative adjective it stays "very", so とてもおもしろくない面白くない is "really boring" – an ordinary description, not an impossibility.

とても or とうてい

とうてい means the same and is used only with a negative. It is more formal and is common in writing; とても is the everyday choice.