"Dein" and "deine" mean your.
You use "dein" for: 1) masculine singular 2) neuter singular.
You use "deine"for: 1) feminine singular 2) all plurals.
Examples: dein Hund (MS) = your dog dein Pferd (NS) = your horse deine Frau (FS) = your woman deine Äpfel (P) = your apples.
That is your apple juice. It is not mine. You will drink it. You will enjoy it.
It is yours.
Thanks, edu22765. I understand the meaning is different. But wouldn't "Der" in "Der ist dein Apfelsaft" refer to a tacit subject as well? Like in "Es ist dein Apfelsaft". Or would that be the same as saying "Der Apfelsaft ist dein Apfelsaft" which is grammatically correct but unnecessarily redundant?
I am afraid this is an ill-defined and complicated situation, and not a useful example for explaining demonstrative pronouns. It kind of boils down to the fact that "dein Apfelsaft" is an 'abstract' concept (this glas of juice over there on the table, this jar I am just serving...) which you wouldn't assign anything but a neuter gender. However, the situation will change already if you compare two sorts of apple juices, for example. "Der schmeckt mir besser" (I like this one better), "der ist süßer" (this one is sweeter) would be valid statements then. As I said, a very vague linguistic area - sorry :-((
I accidentally typed "That is your applejuice" (forgetting to leave a space between apple + juice) and it scored my answer as incorrect. Granted, I did answer with a typo, but considering that other questions/problems accept typos (while pointing them out) it kind of seems unfair to score you wrong.
I suppose it's just part of the learning curve. Not a big deal, but accepting some accidental typos (ex: juxtaposing "ie" with "ei") while rejecting others is weird.
The possessive pronouns are inflected by the case and gender of the noun.
In this example the case is nominative and the noun 'Apfelsaft' is masculine, so the possessive pronoun is dein
If the possession (noun) had been feminine the possessive pronoun would have been deine
z.B. Das ist deine Orange
unlike English, German's substantives actually have genders and different forms depending if they are in: Nominativ, Akkusativ, Dativ, or Genitv form. In this case, the form is Nominativ, so there are only two possibilities: for male and neutral substantives use dein, and for female substantives use deine.
I still can not tell the difference between feminine, masculine and neutral verbs, I do not know if the potato or the moon is a boy or a girl so... and I have been studying German for 2 years and I know it probably sounds totally stupid to someone fluent in German. I also have no one to actually speak German with only read and write.
I am afraid this is something that just needs to be learnt by heart (except for a few indicator endings like -er, -nt, -ur which help in some cases). Try to memorize words including their articles from the start: the moon = der Mond, rather than moon = Mond.
And don't worry too much as use of inappropriate gender is very common with non-native speakers, and it rarely ever compromises the meanings you wish to convey.
You would benefit from looking at a site/page that fully explains the use of possessive pronouns/articles, but in short, with regards to 'ihre', you would use it in Nominative and Accusative cases when:
the possessor is feminine and the object is feminine or plural
their are plural possessors and the object is feminine or plural
her/their dog - ihr Hund
her/their horse - ihr Pferd
her/their cat - ihre Katze
her/their dogs - ihre Hunde
her/their horses - ihre Pferde
her/their cats - ihre Katzen
Explanation from a native ;) : So technically there is none, it is both translated to "das". In cases of saying "this and that" we'd probably say "dies und das" though. You also can make a little difference in some cases by saying "das hier" for "this" and "das da" for "that".
But trust me, just use "das" for both "this" and "that" in any cases.