Translation:She confessed, that she longs for home.
English word "home" is irregular. Home without a determiner (the, a) usually means "the person's home." Esperanto doesn't have this irregularity.
Esperanto, however, does have a rule that possessive determiners (mia, ŝia...) can be replaced with "la" when the connection is obvious and especially when the connection is intimate. "Take my hand" is "Prenu la manon."
Because of both these peculiarities interact with each other, "home" by itself in English is very often the same as "la hejmo."
Sometimes it's "sopiras pri" but here it's "sopiras al." I can understand "sopiras pri" but really do not understand "spiras al." Is the "al" because a direction is implied? Perhaps "sopiras pri" is used when the longing has no geographical direction (as, say, a longing for a spouse, or for love, or for fame), but "al" is used when there is a direction (say, a longing for home or for France)?
It is always a good idea to look, what Plena Ilustrita Vortaro (PIV) says about case government, i.e. what cases and prepositions are used with a particular word. For sopiri PIV says, that the verb is transitive, i.e. takes a direct object.
- Mi sopiras mian perditan feliĉon : I long for/mis my lost happiness.
Since the accusative case can in many cases be replaced by a preposition, the obvious question is what preposition to use with sopiri. Your interpretation about a direction, a movement seems right to me.
In E-o you don't change tense when moving from direct narrative to indirect. So you meet her and she says: Mi sopiras al la hejmo. Later you retell the occasion: Ŝi konfesis, ke ŝi sopiras al la hejmo. In other languages the tenses may be changed, but since the rules of changes vary from language to language, Z chose the simplest way (thank god) not to change at all.
You can report it, I suspect that part of the problem is that "miss" in English has too many definitions. But sopiri just has one; to long for, feel nostalgic for.
So my full answer is that it's "a correct answer" but not the best one. However, if you, as I recommended, click the report button and tell the programmers (who rarely, if ever, read this page) that they missed a meaning, you may get a message back in a few weeks thanking you for improving the course.