Yes you can do that. Basically you would:

A) Rename public_html to something like /archive
B) Then rename /community to /public_html
C) Then move the new public_html from /archive/public_html up one level to the same level as /archive
D) You might have to adjust the settings / configuration in 4images to reflect the new install location.
E) You might have to change permissions on the new public_html to something like 711

or plan B is have support reset your account and start fresh, where you just install 4images from the beginning which may be cleaner.

There are other ways to do this but these are the 2 easiest I suppose.