I would choose (2): Thanks to their good advice, we would have had problems.
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IvanhrThis is certainly not a beginner's question. Yes, the correct answer is "but for"."but for", as used here, means that something would've happened if it hadn't been for something else. So, your sentence could be rewritten asIf it hadn't been for their good advice, we would have had problems. (you should realize that this is a conditional III sentence)The meaning, of
screamererI just want to ask if thanks to could be used and if so, how would it differ in meaning.No, it doesn't work logically here. But you can say