= Solution
Assume sufficient smoothness up to the boundary for uniform Taylor remainders, for example $u\in C^8(\overline\Omega)$ and $f=\Delta u\in C^6(\overline\Omega)$. Direct Taylor expansion of the <nine-point finite-difference stencil> gives
$$
\Gamma_9u=h^2\Delta u+\frac{h^4}{12}\Delta^2u
+\frac{h^6}{360}(u_{xxxxxx}+u_{yyyyyy}+5u_{xxxxyy}+5u_{xxyyyy})+O(h^8).
$$
Thus the normalized <local truncation error> $h^{-2}\Gamma_9u-f$ is $\boxed{O(h^2)}$. The unscaled residual $\Gamma_9u-h^2f$ is $O(h^4)$. Stating the normalization avoids ambiguity in the meaning of truncation order.
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