In the example given in the former answer, Romeo is trying to avoid fighting Tybalt, simply because he is now related to him. However, that isn't Romeo's usual way of dealing with conflict. When it comes to internal conflict, it's a different story.
First of all, whenever he has an internal conflict and he doesn't know how to handle it, he goes to his father-figure in the play, Friar Laurence. Romeo never seeks advice from his father. The Friar is the gentle, supportive, and calming influence in Romeo's life.
Secondly, both Romeo and Juliet are young, impulsive, and emotional. Every time a situation doesn't go their way, they immediately threaten to kill themselves. After Romeo kills Tybalt and is banished from Verona, he seeks shelter in the Friar's cell and and the Friar has to stop Romeo from taking his life.
You might like to answer this question with reference to Act III scene 1, when Tybalt enters looking for a fight with Romeo. Of course, the irony of this scene is not lost on the audience, who have just seen Romeo and Juliet marry, making Tybalt Romeo's kinsmen. Thus Romeo does everything he can to prevent a conflict and to calm down the situation. Note what he says to Tybalt:
I do protest I never injured thee,
But love thee better than thou canst devise
Till thou shalt know the reason of my love;
And so, good Capulet, which name I tender
As dearly as mine own, be satisfied.
He is clearly trying to diffuse the situation by attempting to calm Tybalt down and protest his good will and intent. Unfortunately, he does not feel able at this stage to announce his marriage to Juliet. In response to Mercutio trying to engage Tybalt in conflict, Romeo tries to get Mercutio to "put [his] rapier up," in vain. Thus we can see that Romeo does everything he can in this scene to avoid conflict in what ever way possible. It is only Mercutio's unfortunate death that drives him to distraction and leads him to fight Tybalt, slaying him.