Causality and ROC of a stable LTI system
This looks like homework, so I'll give you a hint to help you figure this out by yourself.

There are 2 poles: one at $z=3$ (i.e., outside the unit circle) and one at $z=\frac13$ (i.e., inside the unit circle). For such a system there are three possible ROCs; one corresponds to an anti-causal system, another one to a causal system, and a third one to a non-causal system with a two-sided impulse response. But only one of those ROCs includes the unit circle, and that's the ROC corresponding to a stable system.