  In this work we construct an effective four-dimensional model by
compactifying a ten-dimensional theory of gravity coupled with a real scalar
dilaton field on a time-dependent torus without the contributions of fluxes as
first approximation. This approach is applied to anisotropic cosmological
Bianchi type II model for which we study the classical coupling of the
anisotropic scale factors with the two real scalar moduli produced by the
compactification process. Also, we present some solutions to the corresponding
Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology and
we claim that these quantum solution are generic in the moduli scalar field for
all Bianchi Class A models. Also we gives the relation to these solutions for
asymptotic behavior to large argument in the corresponding quantum solution in
the gravitational variables and is compared with the Bohm's solutions, finding
that this corresponds to lowest-order WKB approximation.
