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LingakuLingaku[subject] + 何以 + [verb phrase]
不 + [verb phrase]，何以 + [verb phrase]？
何以见得？
何以 is a formal question word: 何 "what" + 以 "by means of". It asks "why" or "how, on what grounds", and it goes after the subject, before the verb. Outside a few fixed phrases it belongs to writing.
The one form you will hear in speech is 何以见得: "how can you tell?", "what makes you say so?". It challenges the other person to back up a claim.
何以 can also ask by what means something is achieved, close to 怎么 or 凭什么.
After a negative condition, 何以 turns the sentence into a rhetorical question with an obvious answer: you can't. This is common in essays and sayings.
Apart from 何以见得, a spoken question takes 为什么 or 怎么. 何以 in a casual question sounds stiff or mock-solemn.