Suppose that $$f(x) = \frac{6}{\left(2x-3\right)^{2}},$$ and that $F$ is an antiderivative of $f$ such that $F(3) = 4$. Find $F(x)$, for $x >{\frac{3}{2}}$.

$F(x) =$ , for $x >{\frac{3}{2}}$.