  In the paper is presented a four-body potential model for $q^2\bar{q}^2$
systems which includes both the spin and flavour degrees of freedom, extending
the formalism presented already in the spin independent situation. This allows
an application to a realistic situation, which is chosen to be $K\bar{K}$
scattering. It is seen that because of the gluonic effects in this multi-quark
system, the $K\bar{K}$ attraction resulting from the quark-exchange mechanism
gets appreciably decreased compared to that emerging through the naive two-body
potential approach.
