I thought that when mögen is conjugated with -en at the end, it is because the subject it is linked to is plural. In addition, I thought that Sie was for either "she" or "they."
Sie can also mean "you". That particular form of "you" is formal and is used for both singular (like "du") and plural (like "ihr"). It is used when addressing your superiors, strange adults, and people you just don't know well. It is considered polite. Sort of like "sir" and "ma'am" I suppose, but a lot more common. There are a few things you need to know about this version of "you".
1) In the nominative and accusative cases it is written "Sie", but it becomes "Ihnen" in the dative case.
2) It is always capitalized (and "Ihnen", the dative form, is also always capitalized). This is important, because this is the clue that often tells you they mean "you" and not "they" (obviously it's not a help in this particular sentence because it's the first word and either would be capitalized anyway).
3) The form of the verb that goes with this "you" is the infinitive form, same as is used with plurals.
Oh, I'd intended to include a link to web page that discusses this in more detail but I forgot. Here it is!
I was told i was correct with "they want the apple" which although it could have similar meaning, is not helping me remember the route verbs
I put "she likes the apple" how could I have known without context the "sie" was referring to "they" not "she" im so confused!