The pdf of the product of two independent random variables X and Y with pfd f(x) and g(y) respectively is given by
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The answers given to you at the other websites you have posted these questions apply here too. Getting the product of two standard normal distributions requires knowledge of the modified Bessel Function of the Second Kind. When the mean of the normal distributions is not equal to zero the question is much tougher.
Why do you want to know how to get these distributions?
There have been other posts asking the same thing in this subforum. Find them and read the links that have been given.