Does my Canon Rebel XT have the capability to produce a picture with resolution of 150dpi @ 240.48" x 74.26"?

Answer 1

The maximum resolution of the XT is 3456 x 2304 - divide this by 150dpi would give you about 23" x 15.4"

Answer 2

Eh... no. You can not produce a medium resolution bill board / wall paper with any digital SLR, any film SLR, or any other kind of camera.
The good news, is that you won't view a 20 foot print up close. And this means that you probably don't really need 150dpi.
With actual bill boards along the freeway you can get away with just 2 (two) dpi.
The XTi has a maximum resolution of 3.456 x 2.304 pixels. Now, 3456 pixels / 241 inches = 14dpi. So you can PROBABLY get a decent result.
If it's for a wall paper, I've seen decent results with 8 megapixels. The picture can be interpolated to avoid pixelization. You obviously can't press your nose to the wall and expect to see tons of detail, but from an arm's length, it'll look pretty good. Just make sure that you select a perfectly sharp image to begin with.
A common tip for this kind of stuff is to use a picture that doesn't have a lot of fine detail in it. E.g., don't select a cityscape with 20.000 houses, windows, cars, people, etc. Don't select a landscape with 700 trees. Those kinds of prints are sure to disappoint - and perhaps even give you a headache.