I have an ATV which has 19 x 7.0 - 8 tires (Rim width is 6 inches) I want to install 18 x 8.5 - 8 tires on these rims. Will this work?

People put wider tires all the time on stock wheels on full-size vehicles. I would guess that probably up to 2" wider would be ok on stock wheels but that's pushing it. It gets to the point that with stock wheels, clearance might be an issue on the back side of the tire, especially on the front. You might not be able to turn the bars fully before the tires start to rub. That's why most aftermarket wheels are offset. It makes the quad wider but that's not always a bad thing. Putting on larger tires raises the center of gravity so making the quad a few inches wider makes it more stable. The only drawback is that tight trails become really tight then. And tires might stick out past the fenders so you'll sling more mud on yourself than with stock tires.