  After we study the 6-dimensional ${\cal N} = (1, 1)$ supersymmetry breaking
and $R$ symmetry breaking on $M^4\times T^2/Z_n$, we construct two ${\cal N} =
(1, 1)$ supersymmetric $E_6$ models on $M^4\times T^2/Z_3$ where $E_6$ is
broken down to $SO(10)\times U(1)_X$ by orbifold projection. In Model I, three
families of the Standard Model fermions arise from the zero modes of bulk
vector multiplet, and the $R$ symmetry $U(1)_F^{I} \times SU(2)_{{\bf 4}_-}$
can be considered as flavour symmetry. This may explain why there are three
families of fermions in the nature. In Model II, the first two families come
from the zero modes of bulk vector multiplet, and the flavour symmetry is
similar. In these models, the anomalies can be cancelled, and we have very good
fits to the SM fermion masses and mixings. We also comment on the ${\cal N}=(1,
1)$ supersymmetric $E_6$ models on $M^4\times T^2/Z_4$ and $M^4\times T^2/Z_6$,
SU(9) models on $M^4\times T^2/Z_3$, and SU(8) models on $T^2$ orbifolds.
