I want to get impulse response of causal system
Several comments:

First, the usual symbol for the Z-transform is $z$ rather than $s$ (which is common for Laplace transform).

It is more common to express $H(z)$ in terms of $z^{-1}$. Note that the causal inverse transform for a single pole at $\alpha$: $H(z) = 1/(1-\alpha z^-1)$ is $h[n] = u[n] \alpha^n$.

So your transform $H(z) = \frac{3}{1 - 1/4 z^{-1} - 1/8 z^{-2}}$ can be expanded to the sum of two terms like the single pole above.