solution: We rearrange the given equation to $|x-4| = 12$.  Thus either $x-4 = 12$, meaning $x = 16$, or $x-4 = -12$, meaning $x=-8$.  Our answer is therefore $16\cdot (-8) = \boxed{-128}$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  In the equation $|x-4| -10 = 2$, what is the product of all possible values of $x$?
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: -128
extra_info.question: In the equation $|x-4| -10 = 2$, what is the product of all possible values of $x$?
extra_info.split: test