Check this out: http://www.grammar-monster.com/easily_confused/youre_your.htm
I read the sentence tu casa es un palacio. But the audio sounded like tu casa es tu palacio. After listening,many times, i translated it as I heard tu palacio. Wrong of course, but they often do that kind of thing where sentences make no logical sense ,or are very difficult to understand.
Within this course? Just pick one. You can also throw vuestro in the mix, they all translate to "your". :)
For real life:
- tu is used with tú (you, singular, informal)
- su is used with Usted and Ustedes (you, singular and plural, formal)
- vuestro is used with vosotros (you, plural, informal, used in Spain)