First, we can simplify the expression inside the parentheses by distributing the negative sign:
$$(\sqrt{3 w-2}-4)^{2} = (\sqrt{3 w-2})^2 - 2(\sqrt{3 w-2})(4) + 4^2$$
Simplifying further, we have:
$$(\sqrt{3 w-2})^2 - 2(\sqrt{3 w-2})(4) + 4^2 = 3w - 2 -
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