Simply : 10 inch x 10 inch print @ 600 dpi = 6000 x 6000px. It's that simple.
Here is a useful calculator: [https://www.pixelcalculator.com/]
All you need to know is that the printer on which your graphic will be printed can manage to squeeze in certain number of dots into a one inch square. To fill this space correctly, you need to produce enough pixels to ideally place one pixel into one dot.
At the time of writing 300dpi is about right for many print applications, but i would encourage you to look to 600dpi, for future proofing your work.
Where I think people get confused is about hardware device PPI. PPI can refer to the "density" of pixels in a device. I.e How closely packed are the pixels in a monitor, or a phone for example. This will affect how the device displays your graphic. If the pixels are dense, then the image will appear much smaller, exactly as with a high dpi printer, printing at high dpi setting, the image will appear much smaller.
Tesujin is correct: "Images don't have a DPI until you print them." They have pixel file sizes only. You need only worry that you have a suitable amount of pixels in your working environment for the print destination device.
I hope that helps.