They start dating.
They have been going out for eight years.
另外，break up指两个恋人或者夫妻分手，我没见过两个普通朋友断交用这个词组的。也许两个普通朋友断交可以说stop contacting with each other, stop speaking to each other.
break up phrasal verb ( END RELATIONSHIP ) phrasal verb
If a marriage breaks up or two people in a romantic relationship break up, their marriage or their relationship ends
Jenny and George have broken up.
She's just broken up with her boyfriend.