To simplify the given expression [tex]\(\frac{12 x^9 y^4}{6 x^3 y^2}\)[/tex], follow these steps:
1. Simplify the coefficients:
[tex]\[
\frac{12}{6} = 2
\][/tex]
2. Simplify the exponents of [tex]\(x\)[/tex]:
[tex]\[
\frac{x^9}{x^3} = x^{9-3} = x^6
\][/tex]
3. Simplify the exponents of [tex]\(y\)[/tex]:
[tex]\[
\frac{y^4}{y^2} = y^{4-2} = y^2
\][/tex]
Putting it all together, we get:
[tex]\[
\frac{12 x^9 y^4}{6 x^3 y^2} = 2 x^6 y^2
\][/tex]
Thus, the equivalent expression is:
[tex]\[
2 x^6 y^2
\][/tex]
The correct answer is:
[tex]\[
\boxed{2 x^6 y^2}
\][/tex]
This corresponds to choice D.
