Answer
Absolutely Convergent
Work Step by Step
Let us apply the Ratio Test to the given series.
$\lim\limits_{n \to \infty} |\dfrac{u_{n+1}}{u_n}|=\lim\limits_{n \to \infty} |\dfrac{u_n\dfrac{-3(n+1)}{2 (2n+3)} }{u_n}| \\=\lim\limits_{n \to \infty} \dfrac{3n+3}{4n+6}\\=\lim\limits_{n \to \infty} \dfrac{3+3/n}{4+\dfrac{6}{n}} \\=\dfrac{3}{4} \lt 1$
This implies that the series is Absolutely Convergent by the ratio test.