Learn Portuguese (Portugal): A duquesa deixou-os falar.

The verb deixar is a causative verb. When the second verb (falar) is intransitive (meaning it has no direct object of its own in this sentence), the person being allowed to do the action is treated as a direct object. Therefore, we use the accusative pronoun -os. If the duchess had let them speak some specific words (adding a direct object), we would use the dative pronoun -lhes for the people.

Why is the pronoun attached to the end of deixou with a hyphen?

In European Portuguese, pronouns default to attaching to the end of the verb in affirmative main clauses. Because there is no negative word, conjunction, or other magnet word before the verb to pull the pronoun to the front, it attaches normally to deixou.

Does the pronoun -os change form because of how deixou ends?

No, it stays as -os. Pronouns only change to -los or -nos when the preceding verb ends in specific consonants (-r, -s, -z) or nasal sounds (-m, -ão, -õe). Since deixou ends in an oral diphthong (a regular vowel sound), the pronoun form does not change.

Why is falar in its basic infinitive form instead of the personal infinitive?

After causative verbs like deixar, mandar, and fazer, the following verb generally remains in the basic impersonal infinitive. The pronoun -os already clearly identifies who is speaking, making a conjugated personal infinitive redundant.