cannot possibly be; hardly~
Expresses that something is so extreme that it cannot be done or is practically impossible.
This pattern emphasizes that the negative statement is absolute. It is often used with potential verbs (like できる, 分かる) or with adjectives to say that the degree is so high that the opposite is impossible. For example, とても信じられない means "cannot possibly believe" or "hardly believable." It is stronger than just saying 信じられない alone.
In conversation, the とても can be replaced by どうしても in some cases, but とても is more common in this pattern. Note that とても here is not the positive "very" meaning; it intensifies the negation. The nuance is often one of surprise, impossibility, or strong emotion.