Learn Romanian: Ei urăsc apartamentul murdar. - They hate the dirty apartment.

Urăsc comes from the verb a urî (to hate). Most Conjugation 4 verbs end in -i and take the -esc suffix (like a citi -> ei citesc). However, verbs that end in -î take the -ăsc suffix instead. For 'they', the form is urăsc.

Would the verb change if the subject was ele (the feminine word for 'they')?

No. Romanian verbs change depending on the person doing the action (I, you, we, they), but they never change based on gender. 'They hate' is urăsc whether the subject is ei (masculine/mixed group) or ele (all-female group).

Where is the word for 'the' in apartamentul?

In Romanian, the word for 'the' attaches to the end of the noun rather than sitting in front of it. Apartament is a neuter noun, so to say 'the apartment', you add the singular ending -ul to the end, making it apartamentul.

Why doesn't the adjective murdar (dirty) change to match the -ul ending on the noun?

In Romanian, the word for 'the' only attaches to the first word in the noun phrase. Because the noun apartamentul comes first, it takes the -ul. The adjective murdar comes after it, so it just stays in its normal singular form to describe the apartment.