Answer
$\frac{3a}{2b}+2a-3.$
Work Step by Step
We divide each term of the polynomial by the monomial as follows
$$
\frac{3a^2b + 4a^2b^2 - 6ab^2}{ 2ab^2}= \frac{3a^2b }{ 2ab^2}+ \frac{ 4a^2b^2 }{ 2ab^2}+ \frac{ - 6ab^2}{ 2ab^2} \\
=\frac{3a}{2b}+2a-3.
$$
