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I'm not entirely sure what you are asking but if your Z-domain representation is $$H(z) = \frac{b_0+b_1 z^{-1}+b_2 z^{-2}}{a_0+a_1 z^{-1}+a_2 z^{-2}}$$ Then your difference equation is $$a_0 \cdot y[n] + a_1 \cdot y[n-1] + a_2 \cdot y[n-2] = b_0 \cdot x[n] + b_1 \cdot x[n-1] + b_2 \cdot x[n-2]$$ And solving for $y[n]$ we get y[n] = \frac{1}{a_0}(b_0 \cdot ...