Learn Farsi: آیا می‌دانید که فارغ‌التحصیلی در کدام گرایش سخت است؟ - Do you know in which specialization graduation is hard?

It is an Arabic-derived compound. فارغ (faregh) means "finished" or "free from," and تحصیل (tahsil) means "education" or "study." The ال (ol) in the middle is the Arabic definite article ("the"), which is preserved in many formal Farsi terms. Finally, the ی (-i) suffix turns it into an abstract noun meaning the act or state of graduating.

Why is there a که (ke) right before the embedded question?

In Farsi, when you embed a question inside another clause (like "Do you know..." + "...which specialization is hard?"), it is very common to connect them with که (that). English drops "that" before a question word, but Farsi comfortably uses it to introduce the subordinate clause.

What exactly does گرایش (gerayesh) mean here, and how else is it used?

While گرایش generally translates to "trend," "tendency," or "inclination," in an academic context it specifically refers to a "specialization," "concentration," or "sub-major" within a broader university degree program.

Could the word order in the second half of the sentence be rearranged?

Yes! You could say ...که در کدام گرایش فارغ‌التحصیلی سخت است؟ Farsi word order is quite flexible. The original sentence places فارغ‌التحصیلی first to establish "graduation" as the main topic, whereas moving در کدام گرایش to the front would place stronger emphasis on "which specialization".