I have an image that I need to enlarge to 84" wide and 72" tall. How can I do this with as little to no pixelation? Is it possible to do this in Corel Photo-Paint X6?
You can't, at least practically speaking.
An image only has so many pixels. To enlarge the photo, you either need to make the individual pixels bigger (it will be noticeably pixelated) or you need to make up extra pixels in between (it will typically be noticeably blurry).
For slight enlarging, the latter is usually acceptable--especially with some careful application of unsharp mask filters and the like.
That said, there is software that claims to be able to make up the extra pixels with smarter algorithms that supposedly reduce the blurriness. Typically done with fractals. I haven't used any of them. There are plenty of options. A quick google search returns many of them, this being but one example: http://www.imaging-resource.com/SOFT/GF/GF.HTM
Beyond that, sometimes you don't need to enlarge the image via software. Large format printing is typically not viewed close up. It's typically viewed from a distance. In that case, you may not need any extra pixels. Yes it will look pixelated if you stand 2' away, but from 20' it may look just fine.