Transfer function of resonant filter with 2 poles, peak at $f_0 = 500\text{ Hz}$, and $\Delta f = 32\text{ Hz}$
You mistyped a few crucial numbers (the coefficients of $z^{-2}$). With the correct coefficients as shown in the link in your question, you quickly see that choice $b)$ can be discarded because it has a third order polynomial in the denominator.

For a peaking resonant filter we need two complex conjugate poles, so we can discard choices $c)$ and $d)$ because they have real-valued poles (due to the negative coefficient of $z^{-2}$). So we're left with $a)$ and $e)$, for which we need to compute the angles of the poles, because this is (approximately) where the frequency response peak will occur. Having obtained those angles we just need to check which one is closer to the angle corresponding to a frequency of $f_0=500\textrm{ Hz}$ (with $f_s=10\textrm{ kHz}$).

So the angle we're looking for is

$$\theta=2\pi\frac{500}{10000}=\frac{\pi}{10}$$

and it turns out that the poles of transfer function $a)$ have just that angle.