Answer
$$\frac{12x^3+9x+4}{2}$$
Work Step by Step
In order to divide monomials, we look for common terms in the numerator and the denominator that can be canceled out. Doing this, we find:
$$\frac{24x^6+18x^4+8x^3}{4x^3} \\ \frac{2x^3\left(12x^3+9x+4\right)}{4x^3}
\\ \frac{12x^3+9x+4}{2}$$
Note, if we wanted to check this answer, we could multiply the answer by the value we canceled out to see if that matched the original numerator.