Right-click on Fallout 4 and click Properties.Here is the common way to see the compatibility of your system and the game this would be the same for all the operating mediums.
If your laptop or computer has a compatibility issue then you would have an issue running fallout perfectly.
Most probably any one of them would help you to come out of the fallout 4 black screen and enjoy the game again. Just try one of them at a time and see which one is going to work for you. It’s not necessary that you have to try all of them. Here are the fixes that you can do to fix the black screen issue. Solutions to Fallout 4 Black Screen Error