{The conditions and consequence that favours the  $$t_{2gg} e_g^1$$  configuration in a metal complex are:

The electronic configuration $$t_{2g}^3 e_g^1$$ corresponds to a $$d^4$$ metal ion.

In a weak field (small $$\Delta_0$$), electrons fill according to Hund's rule, avoiding pairing. So 4 d-electrons go as: $$t_{2g}^3 e_g^1$$ - one electron in each of 3 $$t_{2g}$$ orbitals and 1 in $$e_g$$. This gives maximum spin (high spin complex).

A weak field ligand produces small crystal field splitting, favoring high spin configuration.

The correct answer is Option B: weak field ligand, high spin complex.