Learn Farsi: ما در مورد نتیجه صحبت کردیم، پس این راه‌حل را انتخاب کردیم. - We talked about the result, so we chose this solution.

Yes, both mean "so" or "therefore" and are used to show the result of an action. However, pas is much more common in everyday spoken Farsi, whereas banâbarin sounds a bit more formal, like saying "consequently" in English. In this casual sentence, pas is the most natural choice.

I learned darbâre-ye for "about". Why does this sentence use dar mored-e?

They mean exactly the same thing and are completely interchangeable in this context! dar mored-e literally means "in the matter of," but it is used every day just like darbâre-ye to mean "about." You will hear native speakers use both all the time.

How does the word râh-e hal translate to "solution"?

It is a combination of two words joined by an ezâfe (the connecting "e" sound). râh means "way" or "path," and hal means "solving." So, râh-e hal literally translates to "way of solving," which is the everyday Farsi word for "solution."

Why is the direct object marker râ used after in râh-e hal?

The word râ marks the specific direct object of the verb entekhâb kardim (we chose). Because you are talking about this specific solution (in râh-e hal), the object is definite, so you must use râ immediately after the noun phrase to show what is being chosen.