"She loves this cat."
Translation:Ona kocha tego kota.
There aren't any articles in Polish, ten is a demonstrative pronoun, which corresponds to this/that in English. Like most other parts of speech, it's inflected for gender, number and case.
It this sentence, tego is singular masculine animate accusative.
Take it EASY:
How do you say it in English? "I love he/she?" (wrong...)
or "I (subject) love him/her" (direct object - accusative)?
It is a cat (nominative) - To (jest) kot (kto? co? - Mianownik)
I love the cat (him/her - accusative) - Kocham kota (kogo? co? - Biernik)
Many Polish verbs put the following noun (direct object) in accusative
case, (kogo? co? - Biernik) in affirmative statements. To make it EASY,
the negative statement which requires genitive case (kogo? czego? - Dopełniacz) would need the same word "kota" fo this type of a noun
(Biernik/accusative = Dopełniacz/genitive):
She loves this cat - Kocha tego kota (Biernik/accusative)
She does not love this cat - Nie kocha tego kota (Dopełniacz/genitive)