<h2>Correct answer:</h2><h3>No les gusta comer carne</h3>
In this sentence, tus padres has been replaced by the indirect object pronoun that matches the third person plural, which is les. So tus padres receives indirectly the action of the verb gustar. On the other hand, since after the conjugation of the verb gustar comes an infinitive verb, then the conjugation must match the third person singular, which is gusta. Finally:
<em>- ¿Por qué no les</em><em> gustan</em><em> a tus padres las hamburguesas?</em>
- <em>No les </em><em>gusta</em><em> comer carne</em>