You can find some information about the zoo and entrance fees here:
Shortly, right now the adult entrance fee is 4500 HUF per person while the kid entrance fee is 3200 HUF. There are quite a lot of family tickets available, for example:
2 adults + 2 kids: 13,300 HUF
1 adult + 2 kids: 9400 HUF
1 adult + 3 kids: 11,700 HUF
2 adults + 4 kids: 17,400 HUF
These are some examples, and they are valid as of May 2023. They might change in the future, but these will at leave give you an estimation of what you need to pay as you visit Budapest Zoo.