Like the Pontic sea, whose icy current and compulsive course ne'er keeps retiring ebb but keeps due on to the Propontic and the Hellespont, even so my bloody thoughts with violent pace shall ne'er look back, ne'er ebb to humble love till that a capable and wide revenge swallow them up.
Now, by yon marble heaven , in the due reverence of a scared vow I hear engage my words.
She gives it out that you intend to marry her. Do you intend to?
So, so, so, so! They laugh that win!
Do ye triumph, Roman? Do you triumph?
I marry her! What? A customer? Pritheebear some charity to my wit. Do not think so unwholesome of me. Ha, ha, ha!
Ha. hah, ha!
This conflict above is external. The conflict starts with Desdemona saying she cares for Cassio which triggering anger in Othello and making him slap her. This propels the plot since it makes Othello look abusive in front of Lodovico. To add, this might become a larger issue later and damage Othello's reputation later, and it does not help that Iago hints to Lodovico that Othello is constantly abusive towards Desdemona. The type of conflict is person vs person since Iago is indirectly purposely causing this all to occur.
In the box above Othello is facing an internal conflict. Othello is facing strong emotions of hate, anger, and ragee believing that Desdemona is having an affair. The conflict propels the plot since it will influence Othello's and might lead to him seeking some type of revenge on her. As seen in the previous box, Othello slaps Desdemona because she made it look as if she was having an affair, so he slapped her out of rage. Finally, the type of conflict is person vs self since he is facing his emotions. In this his greatest enemy is the emotions that could later lead him to do irrational things that he will later regret in the drama.
In the following image, the conflict Othello is now facing is external. In the box above, Iago starts the conflict by claiming that Bancia says that she will marry Cassio. Cassio brushes it off as a lie calling her a whore and it would be stupid if he married her. Othello takes this as Cassio's opinion on Desdemona as well since he thinks they are secretly having an affair. Cassio is unknowingly feeding Othello's suspicion and hate for him which is the opposite effect Cassio wants to have on Othello. The type of conflict is person vs person since Iago is manipulating Cassio into making it seem like Cassio has nor respect for Desdemona and just treats her like an object.