Answer
diverges
Work Step by Step
An infinite geometric series converges if and only if $|r|\lt1$, where $r$ is the common ratio. If it converges, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term.
The common ratio is the quotient of two consecutive terms: $r=\frac{a_2}{a_1}=\dfrac{12}{9}=\frac{4}{3}$. $|\frac{4}{3}|=\frac{4}{3}\gt1$, thus it diverges.