How to find $h[n]$ system response of this equation?
To take inverse Z-transform just the expression of H(z) is not enough. The inverse could be left sided or a right sided sequence depending on the causality of the system. Also stability of the system can give a clue. For example if the system is stable, the ROC will include the unit circle. Based on these additional information you should now find out right sided or left sided sequence from your partial function expansion. Your system seems to be anti-causal. So you can now work out the math and ask more questions if you get stuck.