How can I obtain x(n) given y(n) and h(n) of a system using Z-Transform?

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I'm given with an output sequence $y(n)$ and impulse response of the system $h(n)$. I have to obtain the input sequence $x(n)$.

My idea is $$y(n) = x(n)\ast h(n)$$

Taking z-transform on both sides and then it becomes $$Y(z)=X(z)H(z)$$

Here after I don't know how to get $X(z)$. I'm not sure whether I could do simple division with $Y(z)$ and $H(z)$

The given sequences are

$$y(n)=\{8,22,11,31,4,12\}$$

$$h(n)=\{2,5,0,4\}$$

Please give me an idea to proceed further. Thankyou :)