Screen has gone bad. Replacing the front panel will fix the issue.
Guide to replace screen:
iPhone 6 Front Panel Assembly Replacement
You can get the screen from here if you do choose to do it yourself:
iPhone 6 LCD Screen and Digitizer Full Assembly
You have a few options, take it to a mobile phone repair shop to get the screen replaced (I would avoid shopping malls as they are generally either expensive or not very well experienced in mobile phone repairs).
Or you can choose to do it yourself which is fairly simple if you follow the steps in the guide well. Parts that you need to be careful in specifically are the metal plate for the screen connectors on the logic board (phillips head screws are different sizes for a reason), removing the home button, metal plate for front panel which has the home button extension cable together and the front camera requires some delicate prying.