The face side of any fabric refers to the one intended, by the designer and the weaver, to be seen; it is usually–but not always–the sleekest looking side. The choice of right side however, is yours alone, it’s just the side you prefer to see.
Only occasionally is there a technical reason that one particular side should be more suited to the work than another.
Sometimes if some extra help is needed, you can tell the intended right side by the pinholes created by tenter hooks along the selvedge.