  The light gluino (12 - 16 GeV) and light sbottom (2 - 6 GeV) scenario has
been used to explain the apparent overproduction of b-quarks at the Tevatron.
This scenario also predicts the decay Z -> b b-bar ~g ~g where the gluinos
subsequently decay into b-quarks and sbottoms. We show that this can contribute
to the width Gamma_4b = Gamma(Z -> b b-bar b b-bar) since most of the sbottoms
and b-quarks arising from gluino decay have a small angular separation. We find
that while no excess in Gamma_4b is observable due to large uncertainties in
experimental measurements, the ratio Gamma(Z -> b b-bar ~g ~g)/Gamma(Z -> b
b-bar b b-bar) can be large due to sensitivity to b-quark mass, the sbottom
mixing angle and the gluino mass. We calculate it to be in the range 0.05 -
0.41 inclusive of the entire parameter space.
