its hard to me to tell what this means formally(as I said I am not expert).
There is no "interpret" operator in zfc.
I believe what it says if you add some robinson axioms + some logical rules on top of zfc, you can carry your results.
It's the same way you don't need to have GCD in stdlib to say that you can compute GCD in C++. You can make your own using parts given.
You don't need to add any axioms, you just build some sets to represent numbers and make operations that act the same way as arithmetic, define some equality relations. Then you derive rules of arithmetic for your handcrafted arithmetic using ZF axioms and you're good. You get axioms of arithmetic derived from your regular axioms without adding them as new axioms to your theory.
You make relations and functions out of sets and prove theorems about them, reducing definition of things in terms of belonging to a set. This isn't particularly complicated.
No, once you start formalize this, it becomes complicated. There is a reason why looks like there is no "peano can be derived from zfc" theorem which would close dispute, and my opponents need to throw links on bro math from stackexchange in this discussion.
its hard to me to tell what this means formally(as I said I am not expert). There is no "interpret" operator in zfc. I believe what it says if you add some robinson axioms + some logical rules on top of zfc, you can carry your results.