If the two couples start as a two-faced line (with the couples facing opposite directions), everybody can keep holding hands. They all just walk forward around the center of the line.

If the the couples start as a one-faced line (with everybody facing the same direction), they must drop hands in the center. The couples turn toward each other and "pass right shoulders" to get to their new spots.

Take care not to confuse Couples Trade with Partner Trade. In a Couples Trade, the couples are the units that are trading -- the dancers in each couple stay together, holding hands, and turn around halfway as a unit. In a Partner Trade, the individual dancers are the units -- the two partners who make up a couple are switching places with each other, and turning around individually.