Learn Farsi: من نمی‌توانم این لکه‌ی بزرگ را با دستمال پاک کنم. - I cannot wipe this big stain with a cloth.

Because it follows نمی‌توانم (I cannot). In Farsi, when you use verbs that express ability, desire, or necessity, the second verb must be in the subjunctive mood. It is similar to saying I am not able that I wipe.

Doesn't the subjunctive usually start with بـ? Why is it missing in پاک کنم?

پاک کردن (to wipe or clean) is a compound verb made of پاک and کردن. With compound verbs, Farsi speakers usually drop the بـ prefix in the subjunctive. So instead of پاک بکنم, it is much more natural to just say پاک کنم.

Why is there a ی at the end of لکه in لکه‌ی بزرگ?

That is the ezāfe, the grammatical link that connects the noun لکه (stain) to its adjective بزرگ (big). Because لکه ends in a vowel sound (the silent letter heh), the ezāfe takes the form of a y-sound to bridge the gap, written here as ی.

Why does را come after بزرگ instead of right after لکه?

The object marker را must follow the entire direct object phrase. Since the direct object here is the full phrase این لکه‌ی بزرگ (this big stain), the را is placed at the very end of it, right after the adjective.