Learn Farsi: آیا دادستان دیروز در دادگاه دیدت؟ - Did the prosecutor see you in court yesterday?

It is made of two parts: did (he/she saw) and the pronominal enclitic -at (you). In Farsi, you can attach these pronoun endings directly to the end of a verb to act as the direct object, completely replacing the need for a separate pronoun and object marker.

Since didat ends with a 't' sound, how do I know it doesn't mean "you saw"?

This is a very common mix-up! Remember that the regular subject ending for "you" in the past tense is -i, making "you saw" didi. The ending -at is specifically an object pronoun. The verb itself is just did (3rd person singular past tense, meaning "he/she saw"), which correctly matches the subject of our sentence, dâdestân (the prosecutor).

Could I say torâ did instead of using the enclitic -at?

Yes, absolutely. Saying torâ did (or the colloquial toro did) means the exact same thing. Using the enclitic on the verb is just another very common, natural way to express the direct object without using râ.

The words dâdestân (prosecutor) and dâdgâh (court) both start with dâd. Is that a coincidence?

Not at all! dâd is a Persian word meaning "justice" or "law". The suffix -gâh indicates a place, making dâdgâh the "place of justice" (court). Similarly, dâdestân combines roots to describe the person taking charge of the law (the prosecutor).