Learn Farsi: پادشاه برایش این عمارت باشکوه را ساخت. - The king built this magnificent mansion for him.

Using the lesson's target structure of چه (che) + Adjective + Noun + indefinite ی (-i), you would change این عمارت باشکوه to چه باشکوه عمارتی (che bā-shokūh emārati!). The full sentence becomes پادشاه برایش چه باشکوه عمارتی ساخت! Notice that we drop the definite object marker را (rā) because the exclamatory structure makes the noun phrase indefinite.

What exactly is برایش made of, and could we write it as two separate words?

برایش combines the preposition برای (for) and the third-person singular enclitic pronoun ـَش (-ash, meaning him/her/it). Because برای ends in a vowel, a 'y' sound bridges the gap, making it barāyash. You could absolutely write it as two separate words: برای او (for him/her). Attaching the enclitic pronoun is just a very common way to make the sentence flow more smoothly.

How is the adjective باشکوه (magnificent) formed?

It is a compound adjective made from the preposition با (with) and the noun شکوه (glory or splendor). Farsi frequently builds adjectives using this 'preposition + noun' pattern. So عمارت باشکوه literally translates to 'mansion with splendor'.

Why does the definite object marker را come after باشکوه instead of right after the noun عمارت?