These questions are from a topic called 'z-transform'.
There's dots for zeros and crosses for poles in this diagram. Since zeros are roots of numerator, and poles are roots of denominator, so I think the function should be:
$$\frac{(z^{20}-1)(z-0.8)}{z^{21}}$$
There's a 21 written in the diagram close to the cross, so I guess that notation means that there are 21 poles, and all are 0. That's why I have $z^{21}$ in my denominator.
Simplifying this function gives
$$\frac{z^{21}-0.8z^{20}-z+0.8}{z^{21}}$$
$$=\frac{0.8z^{-21}-z^{-20}-0.8z^{-1}+1}{(z^{-1})^0}$$
Here, the numerator and denominator are both polynomials in $z^{-1}$ as required. The highest power of $z^{-1}$ in the numerator is 21 and in the denominator is 0.
But the problem is that we can multiply both the numerator and denominator by $z^{-k}$, $k$ from 1 to infinity, and the function remains unchanged. So there's no limit for the highest power of $z^{-1}$ in the numerator and denominator, and it seems like there's no maximum (which the questions are asking for). What am I doing wrong?