"Tú puedes vender tu casa."
Translation:You can sell your house.
Here is a pretty good list as of Sep 2017: http://www.helloworld.com.es/english/quick%20reference/verbs/SpanishVerbList.htm
I would argue that there are significant differences between house and home in English. There are many places where you could not substitute one for another. Generally speaking casa is house and hogar is home. There is an exception however. Those expressions in English where the word home is without an article liking being home, going home or staying home are translated as casa. This is because that is the word that is used on those similar occasions. These expressions generally refer to the place where you live (although still not always a house) .
"Tú" is the personal pronoun "you". "Tu" is the possessive pronoun "your".
"Tú" is not really needed. Puedes vender tu casa. "Puedes" already means, "you can". It is used for emphasis... something like:
I won't do it, but YOU can sell your house. No voy a hacerlo, pero tú puedes vender tu casa.
If you see a one syllable word in Spanish with an accent that is a good indication that there is another one without. The same is true of multisyllable words with an accent over the syllable that would normally be stressed based on the two basic rules of which syllable is stressed. I havent yet found another word for más (e.g.without the accent) so I don't know whether this is the proverbial exception to the rule, an archaic word, or simply my ignorance.
It is always a little difficult to be sure quite what that question is because the same sentence might appear as translation in either direction or to write from hearing etc. But the sentence I see is Tú puedes vender tu casa. If you were asked to translate You can sell your house the options are the sentense listed or Usted puede vender su casa or Ustedes pueden vender su casa (to a couple for example). So you could use su but only if the Subject preposition "matched" it. If you used su casa with Tú that would no longer be translated as your, but rather as his, her or their.
You don't have to use Tú. If Duo marked Puedes vender tu casa as wrong, you should report it. But, although subject pronouns are routinely omitted when form or context makes them clear, there are also circumstances where they are used, mostly for some sort of emphasis (Perhaps the speaker is not able to sell their house) . Of course the main problem that most English speakers have when the subject pronoun is present is when it comes after the verb in a declarative sentence.
That would mean you can sell his or her house. The possessive pronoun must match the Subject pronoun or at least the conjugation. So if you address someone with Tú you would refer to their things also with tu. If you refer to someone with usted, you would use su, but that would be Usted puede vender su casa. But while su can mean your, it will only work with usted. Otherwise it would be assumed to refer to some third person.
Excellent question because it goes to the heart of one of the functions of this accent in Spanish. The accent has three functions. The one shown here is to distinguish between two different words that are written the same. In this case between the subject pronoun tú (you) and the possessive adjective tu (your). If the word is a one syllable word like this, the presence of an accent means that there is another word without one. The most common example is probably él (he) and el (the). All the interrogative pronouns have accents. This distinguishes them from the related relative pronoun, so you will also see those both ways.
Another common use of the accent is to move the syllable stress to another syllable. Spanish has two set rules for stress. If the word ends in a vowel, an n, or an s, then the accent is on the penultimate (next to last) syllable. If it ends in any other consonant, then the stress is on the last syllable. If the actual stress is on any other syllable, it always has an accent to show where the stress is. This explains why all the words ending in cion have the accent in the singular but not in the plural. Acción and producción but acciones and producciones.
The final function of the accent is to break a dipthong into two syllables. You see and hear this most commonly in the difference between words ending in cia and those ending in cía.