Simple Difference Equation Question
Consider definition of H(z), it is the output of a LTI system when input is δ[n]. 

So,in order to determine y[n] at x[n]=δ[n], we have to determine only h[n]. 

First of all, take Z-transform of the system transfer function.





Re-arranging terms, 



Now, we can solve this equation using partial fraction



Taking inverse Z-Transform:




In the 3rd equation, H(z)=Y(z)/X(z)