Learn Farsi: باید این سکه را به کلکسیون خود اضافه می‌کردی. - You should have added this coin to your collection.

When you combine باید (bayad - must/should) with a verb in the past continuous tense, it creates the meaning of 'should have' done something. It expresses an unfulfilled obligation in the past, which is a very common structure at this level.

The current lesson is about the indefinite یک ... ی (yek ... -i). Why doesn't this sentence use that structure?

Because the object here is strictly definite. You are talking about this specific coin (این سکه), not just 'a certain coin' (یک سکه‌ای). Since the demonstrative این (this) makes the noun definite, it takes the definite direct object marker را (ra) instead.

Why use خود (khod) instead of just adding a possessive ending like کلکسیونت (kolleksion-at) for 'your collection'?

While کلکسیونت is grammatically fine, Farsi strongly prefers using the reflexive pronoun خود (self/own) when the owner is the same as the subject of the sentence. Here, 'you' are adding to 'your own' collection, making خود the most natural choice.

How does the compound verb اضافه کردن (ezafe kardan) work with the preposition in this sentence?

To say you add something to something else, you use the preposition به (be). So the structure is [Object] را به [Destination] اضافه کردن ([Object] ra be [Destination] ezafe kardan).