How to know the filter order
If the discrete-time filter is described by the linear difference equation

$$y[n]=\sum_{k=1}^{K}a_ky[n-k]+\sum_{m=0}^{M}b_mx[n-m]$$

(with $a_K\neq 0$ and $b_M\neq 0$), the filter order is given by
$\max\{K,M\}$, i.e., by the maximum delay necessary to implement the filter.