Answer
Not conservative
Work Step by Step
When $F(x,y)=ai+bj$ is a conservative field, then throughout the domain $D$, we get
$\dfrac{\partial a}{\partial y}=\dfrac{\partial b}{\partial x}$
Here, $a$ and $b$ are first-order partial derivatives on the domain $D$.
Here, $a=3x^2-2y^2$
Then, we have $a_x=-4y$
and $b=4xy+3$ so, $b_y=4y$
Therefore, $\dfrac{\partial a}{\partial y} \neq \dfrac{\partial b}{\partial x}$
Thus, the vector field $F$ is not conservative.
