The product of the digits of 3214 is 24. How many distinct four-digit positive integers are such that the product of their digits equals 12?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The product of the digits of 3214 is 24. How many distinct four-digit positive integers are such that the product of their digits equals 12?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
36
The product of the digits of 3214 is 24. How many distinct four-digit positive integers are such that the product of their digits equals 12?
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