Colloquial form of 'どれだけ' meaning 'how much' or 'to what extent' (very casual/slang).
どんだけ宿題があるの？
How much homework is there?
彼、どんだけ寝不足なんだろうね。
I wonder how sleep-deprived he is.
これ、どんだけ時間かかるの？
How long is this going to take?
Used as an interjection expressing surprise or exasperation (similar to 'oh my god' or 'what the...'), with a rude/strong tone.
どんだけ〜！そんなに食べられるの？
What the —! Can you really eat that much?
彼の言い訳、どんだけひどいんだよ。
His excuses are unbelievable.
どんだけ勉強しても合格できないの？（皮肉）
How much do you have to study and still not pass? (sarcastic)