Heterotic supergravity with (1+3)–dimensional domain wall configurations and (warped) internal, six dimensional, almost-Kähler manifolds X are studied. Considering on ten dimensional spacetime, nonholonomic distributions with conventional double fibrations, 2+2+...=2+2+3+3, and associated SU(3) structures on internal space, we generalize for real, internal, almost symplectic gravitational struc...