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 $16\cdot (-8) = \boxed{-128}$.
<|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

user
-128
In the equation $|x-4| -10 = 2$, what is the product of all possible values of $x$?
test