Consider the polynomials:
\[ P(x) = (x + \sqrt{2})(x^2 - 2x + 2) \]
\[ Q(x) = (x - \sqrt{2})(x^2 + 2x + 2) \]
\[ R(x) = (x^2 + 2)(x^8 + 16) \]
Find the coefficient of \( x^4 \) in \( P(x) \cdot Q(x) \cdot R(x) \).

Let's think step by step and output the final answer within \boxed{}.
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