sat-dog

Choice C is correct. Applying the distributive property to the given expression yields $d\left(8d^2-3\right)-6\left(8d^2-3\right)$. Applying the distributive property once again to this expression yields $\left(d\right)\left(8d^2\right)+\left(d\right)\left(-3\right)+\left(-6\right)\left(8d^2\right)+\left(-6\right)\left(-3\right)$, or $8d^3+\left(-3d\right)+\left(-48d^2\right)+18$. This expression can be rewritten as $8d^3-48d^2-3d+18$. Thus, $\left(d-6\right)\left(8d^2-3\right)$ is equivalent to $8d^3-48d^2-3d+18$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.