How does the scene below in Romeo and Juliet demonstrate that hate can be caused by love and can be overcome by it?
Lord Capulet arranges a party for those who favor him and to possibly develop love between Juliet and Paris, but when Romeo arrives, Tybalt become hateful as he is a Monatague.(I.v.)
If I understand your question correctly, you are asking about the relationship between hate and love as expressed in the part of the scene you have identified. Let us focus on how Tybalt responds when he realises that the person he sees is Romeo:
Now, by the stock and honour of my kin,
To strike him dead I hold it not a sin.
It is interesting that Tybalt justifies his hatred and the violence he itends to do upon the person of Romeo by refering to the love that he has for his family. It is the family bonds of "stock and honour" that cause his hatred to be expressed, yet at the same time it is his love for his Uncle, Lord Capulet, that shows how love can overcome hate, when Capulet tells his nephew to not assail Romeo:
Therefore be patient; take no note of him.
It is my will, the which if thou respect,
Show a fair presence and put off these frowns,
An ill-beseeming semblance for a feast.
Tybalt withdraws in anger at his uncle's request, but he recognises that his love and the duty he owes his uncle overpowers his desire to express his hatred.