[Vuejs]-Trying to change data vue.js

Ok I think youve got yourself confused about what is doing what. Your App.vue component and your main.js vue instance each have their OWN instance of the data property. If you want your main.js to be able to pass data into your component you need to expose a prop to do this in. If you want your app.vue component to be able to communicate with your main.js vue instance then you must raise an event and main.js must be listening for that event. I would highly suggest that you spend a day or two with the vuejs documentation. Its honestly some of the best software docs I have ever come across, and your problem is addressed pretty early on in the tutorial.

https://v2.vuejs.org/v2/guide/