Learn Russian: Мой брат работает там три года и два месяца. - My brother has been working there for three years and two months.

This happens because of the numbers. After the numbers 2, 3, and 4, Russian requires the noun to be in the genitive singular form. The dictionary forms are masculine nouns год (year) and месяц (month), and adding -а makes them genitive.

Why is the present tense работает translated as "has been working"?

In English, we use "has been working" to show an action started in the past and is still happening now. Russian is much simpler: if the action is still happening right now, you just use the present tense! Since he still works there, работает is used.

Is the word два (two) used for all nouns?

Not quite! The number two has different forms depending on the noun's gender. We use два here because месяц (month) is masculine (as is год). If you were counting a feminine noun, you would use две. The number three (три) stays the same for all genders.

How come there is no Russian word for "for" in this sentence?

When talking about how long an action has been going on (duration), Russian doesn't use a preposition like "for". You simply state the amount of time directly, which is why we just say три года и два месяца without any extra connecting words.