(-3x^4y^2)^3 s implify: -9x^12y^6 -9x^64y^8 27x^7y^5 -27x^12y^6

To simplify the expression $(-3x^{4}y^{2})^{3}$, we need to apply the power of a product rule, which states that $(ab)^n = a^n b^n$.

1. Apply the exponent to each part inside the parentheses:
$(-3)^{3} (x^{4})^{3} (y^{2})^{3}$.

2. Calculate each part:
- $(-3)^{3} = -27$,
- $(x^{4})^{3} = x^{12}$,
- $(y^{2})^{3} = y^{6}$.

3. Combine these results:
$-27x^{12}y^{6}$.

Therefore, the simplified expression is $-27x^{12}y^{6}$. The correct answer is:

$-27x^{12}y^{6}$.