Good question. Short answer: "into the/an inn" would be in cauponam in Latin.
The Latin preposition in can be translated to English as both "in" and "into" because it can have either meaning in Latin.
When describing the location where something is happening, Latin uses in + ablative case. There is no connotation of any movement, e.g. in dormitorio dormio ("I am sleeping in a room"), in foro loquitur ("she talks in the forum"). In "true" Latin, the ablative singular form of caupona would end with an "a with macron", i.e., ā; unfortunately, Duolingo does not require (or even acknowledge) this in its Latin course (as of 2021-01-28, at least).
On the other hand, just as "into" in English implies some degree of movement or directionality (both physically and figuratively), Latin uses in + accusative case for similar purposes, e.g., in dormitorium ambulo ("I walk into a room"), in forum currit ("she runs into the forum"). In Latin, the accusative singular form of caupona ends with am, i.e., cauponam.
To (finally) answer your question, the reason why you can't translate the Latin sentence given in this exercise as "I throw the/an egg into the/an inn" is because the prepositional phrase in caupona indicates that the subject of the sentence (ego) currently is in the act of throwing (iacio) the object of the sentence (ovum) while the subject is physically located in a specific place (in caupona).
Note that this Latin sentence could be modified easily to mean, instead, "I throw the/an egg into the/an inn" by changing the word caupona to cauponam, i.e., Ego ovum in cauponam iacio.