Minimal number of hyperplanes needed to separate sets of points from one other set
Your problem is NP-complete, even in the following two highly restricted cases:


The dimension $d$ is part of the input, and the question is whether you can separate set $B$ from set $G$ by $k=2$ hyperplanes.
The dimension is $d=2$ (and the number $k$ of separating hyperplanes is part of the input).


This has been proved in:


  Nimrod Megiddo
  On the Complexity of Polyhedral Separability
  Discrete and Computational Geometry 3, pp 325-337, (1988).