Possibility: impossibility
とても~ない
Means “cannot”. This form implies a strong impossibility. Used with negative verbs, often in potential form.
Examples
苦い食べ物はとても食べられない。 I cannot eat bitter food.
ものか・もんか
V (る)
い-Adj
な-Adj + な
N + な
+ ものか・もんか
Means “there’s no way it will happen”, “absolutely not”, “as if”. Expresses disagreement or disbelief.
Example
こんなたくさん家事をするものか。。。無理です。 There’s no way I could do so much housework… It’s impossible.