Possessives match the thing being owned!
In French, all possessives match the gender and number of the thing being owned. Possessives do not match the owner, as they do in English.
For instance, "her lion" would be "son lion" because "lion" is masculine, even though the owner is feminine. Similarly (for number), "ses lions" is "her lions".
Note that "son lion" can also mean "his lion" or "its lion", since we don't get any clue to the gender of the owner from this. We do, however, know the number of the owner. For instance, "son" refers to a singular owner, while "leur" refers to plural owners.
To summarize, for one owner of any gender (given for 1st/2nd/3rd-person):
- Use "mon/ton/son" when one masculine thing is owned. (Note: this is also used for any gender when the next word starts with a vowel, in order to create a liaison.)
- Use "ma/ta/sa" when one feminine thing is owned.
- Use "mes/tes/ses" when multiples of something are owned, regardless of gender.
- Note that "mon", "ma", and "mes" all translate to "my".
And for multiple owners:
- "Notre/votre/leur" for one of something regardless of gender.
- "Nos/vos/leurs" for multiples of something regardless of gender.
- These translate to "Our/your/their".
Similarly, all other determiners in French (e.g. articles) match the gender and number of the noun they are most closely associated with.
You're welcome! "Ton" and "votre" are distinct, and their uses are limited by context. However, Duo doesn't provide you with the requisite context, so both are generally acceptable. The reason for this is that we can't distinguish between singular and plural forms of "you" in English. However, if you're having a conversation, you have to choose between "ton" (one owner) and "votre" (multiple owners) based on context.