Learn Farsi: خوشبختم، خانم. - Nice to meet you, ma'am.

It literally means I am fortunate or I am lucky. It is made of خوش (good), بخت (luck or destiny), and the verb ending ـم (I am). Farsi speakers use this phrase exactly like Nice to meet you in English.

Why is the I am ending ـم attached directly to the word?

In Farsi, the present tense of the verb to be is usually shortened to a suffix and attached right to the end of the noun or adjective. Instead of a separate word for am, you just add ـم to the end of خوشبخت.

Can I use خانم by itself to mean ma'am just like in this sentence?

Yes! While خانم is often used with a last name to mean Ms. or Mrs., you can also use it completely on its own as a polite way to address a woman, exactly like ma'am in English.

How would I say this to a man?

The greeting خوشبختم stays exactly the same regardless of who is speaking or being spoken to. To say this to a man, you just replace خانم with آقا (sir or Mr.), making the sentence خوشبختم، آقا.