The first polynomial remains the same as there is no sign in front of it. The second polynomial is subtracted, so we change the sign of each term inside the parentheses. This gives us:
$$-4 y^{2}-3 y+8 - (2 y^{2}-6 y-2) = -4 y^{2}-3 y+8 - 2 y^{2}+6 y+2$$
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