Learn Farsi: می‌خواستم دوربین جدید را بخرم، ولی نخریدمش. - I wanted to buy the new camera, but I did not buy it.

This is exactly what we are learning in this lesson! The -ash is a pronoun ending meaning "it" (referring to the camera). Instead of saying ân râ nakharidam (I didn't buy it) with a separate word for "it", Farsi speakers often just attach -ash directly to the end of the verb nakharidam (I didn't buy) to act as the direct object.

Why do we use bekharam for "buy" in the first half, but nakharidam in the second?

In the first half, "buy" follows the verb mi-khâstam (I wanted). In Farsi, verbs following "wanting" or "needing" take the subjunctive mood, so we use bekharam (literally: "I wanted that I buy"). In the second half, you are simply stating a factual event that happened in the past, so you use the standard simple past tense nakharidam (I didn't buy).

Why do we need the word râ after durbin-e jadid?

râ marks a specific direct object. Because you wanted to buy "the" new camera (a specific one you had in mind, or one already mentioned), it needs râ. If you just wanted to buy "a" new camera in general, it would be yek durbin-e jadid without râ.

Why is there an "e" sound connecting durbin and jadid when speaking, even if it's not written?

That invisible "e" sound is the ezâfe. It is a grammatical connector used to link a noun to its adjective (camera + new). Even though it's usually not written in the Farsi script, you must pronounce it to connect the words together: .