OK so this is the onboard graphics "card" ie. the basic video output from the motherboard and not an actual separate graphics card.
I get this warning too when starting Premier but I know I have a separate, more powerful graphics card in my machine so I happily ignore it every time. (Click the red continue in the bottom right of the dialog) Premier then works fine.
Do you know for sure if you have a separate card installed?
Press windows + r and then type: dxdiag
Click yes / ok to any warning
Along the top there should be a "Display" tab for each monitor you are running. Check the "Name" field on each of these. For me it looks like this
View attachment 114007
All my screens are connected to NVIDIA GeForce GTX 970
So for you, if this isn't "Intel(R) HD Graphics 4600" then just ignore the warning on start up. (You can disable the warning in Premier under
Edit > Preferences > Genreal > Show system compatibility on start up )
If it does show Intel(R) HD Graphics 4600 then check your monitor is connected to the right output on the back of the PC.
If there is no other port on the back of the PC then you'll need to buy a graphics card. I'm not best placed to recommend one - mine is a few years old and will need upgrading in another year or two so I'll be reading up on them then only!
Good luck!