"I do not hear that cat."
Translation:Nie słyszę tamtego kota.
tam= there, a place. opposite of tu=here.
Tamten/tamto/tamta etc. - different case and gender variants of that/those=the, before a noun, rarely alone.
You can think tamten= tam+ten, etc, most in most cases it works , only accusative female tętamtą.
declension ( masculine noun can have accusative= genitive or accusative= nominative, accusative form of "this"/ "that" need to match)
If you want a simple way to tell when to use which case, there isn't one. But subject is always in Nominative, direct object is often Accusative, and direct object of negation is often Genitive, and never Accusative
It should also be noted there is a incompatibility in conceptual distance between Polish and English:
Polish: ten; ten; tamten
English: this; that; that
So, eng. "this" is always "ten" in Polish, but pol. "ten" can be eng. "this" or "that", while pol. "tamten" is always "that".
This can possibly be made less confusing when you compare historical versions of those languages:
Middle Polish: ten; ów; tamten
Early Modern English: this; that; yonder
In Polish, demonstrative "ów" merged with "ten", but in English "yonder" merged with "that".
(also, note that "ów" is still sometimes used in literature and some Polish dialects/gwaras, but usually no longer carries the meaning of not as close as "ten", but not so far as "tamten", AFAIK)
In Polish words don't just have different genders, but also grammatical cases, depending on the function the word fulfills in a sentence (just like English he/his/him are three different forms of the same word).
Here "tamtego kota" is the genitive form of "tamten kot". One case may add one of few possible endings to a word, depending on the specific word, so even if the gender and case of two words may match, their endings don't have to.