Mhhh maybe someone else can judge your graphics card better but 6GB RAM is mighty low for Fallout 4 :/
Think mimimum is 8GB.
Hardware Requirements are posted for a reason. If you ignore them, you get poor performance or a game that doesn't run at all.
Requirements are 2.8GHz Intel/3.0GHz AMD; 8GB of RAM; Nvidia 550 Ti/AMD 7870 2GB VRAM.
You don't meet any of the requirements.
Yes unfortunatly you are below min required specs in all aspects(GPU,CPU and RAM) so you can not expect the game to run anyhwere near decent even on low settings, what might help you a bit is certain mods for optimized low end settings(you might have to wait for GECK release for those, honestly i dont know since i never searched for them but its not like you have anything to lose since due to your computer the game is more or less unplayable anyway)
Radeon HD graphic is just too weak. For testing purpose, on a Radeon HD8490, I ran the game thru a portable USB3 harddisk. At 1080p, 6fps. Lowest 800x450, 22fps ...
Your processor/GPU APU just isn't good enough. You're also lacking 2GB RAM, I'd say you're pretty much due for an upgrade.
Should i ask at what resolution do you play Skyrim, and what frame-rates do you get?
Also what's you mean with this? APU with Radeon HD Graphics 1.50 GHz