Minimum system requirements are usually not an absolute threshold. They're largely determined by what the developers feel would provide an acceptable quality of gameplay.
Win7/8/10 technically require only 2GB-4GB of RAM, although 4GB-8GB is better and will prevent the OS from bogging the system down.
A game (like Fallout 4) which requires 8GB will probably still run on your system. But it might be slow and stuttery and chunky, it might look awful or be too sluggish and jerky to play or suffer from random slowdowns or simply crash quite often. Or it might still be quite playable, provided some quality settings are turned down a notch. You would probably have to work harder to finish the game and you wouldn't have any real chance in multiplayer sessions.
You can disable running apps and processes to free up (Windows) system resources for the game, it might then run well enough to enjoy. Chances are you'd do much better with an 8GB or 16GB memory hardware upgrade - especially since the upgrade would let you run new games for years to come.
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