Breakdown of Tu aurais dû le vendre à ce courtier.
tu
you (informal singular)
avoir
to have
ce
this (before a noun)
à
at / to / in (general locations) / about (what one thinks about / reacts to)
Questions & Answers about Tu aurais dû le vendre à ce courtier.
How does aurais dû mean "should have"?
Aurais dû is the past conditional of the verb devoir (to have to / must). While the present conditional (tu devrais) means "you should", putting it in the past conditional expresses a reproach or regret about something that didn't happen: "you should have". It is formed with the conditional of avoir (tu aurais) plus the past participle of devoir (dû).
Why is the pronoun le placed right before vendre instead of at the beginning of the sentence?
When a conjugated verb is followed by an infinitive (like vendre), object pronouns usually go immediately before the infinitive they belong to. Because you are selling "it" (le), le goes right before vendre, not before the auxiliary verb aurais.
Since the verb is vendre à (to sell to), why do we use the direct object pronoun le instead of the indirect lui?
Le stands for the thing being sold ("it"), which is the direct object. The person being sold to is the indirect object, which is explicitly written out here as à ce courtier (to this broker). If you wanted to replace the broker with a pronoun and say "You should have sold it to him", you would use both: Tu aurais dû le lui vendre.
Why does the past participle dû have a circumflex (little hat) on it?