Answer
$$3a^2+a^3b^3+4$$
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:
$$\frac{12a^3b^2+4a^4b^5+16ab^2}{4ab^2} \\ \frac{4b^2a\left(3a^2+a^3b^3+4\right)}{4ab^2} \\ 3a^2+a^3b^3+4$$
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.