The exact solution of the 6x6 normal reversi game has already been published (see The solution for the 6x6 Othello board (Joel F. Feinstein and MODOT)). So we know that the C2B4 leads to a +4 result for white and black cannot win. But what about the two other valid moves: C2D2 and C2B2?
Tothello calculated the outcome of these two board positions too: C2D2 is still a winning position for white, leading to a minimum +2 final result (white wins) whilst C2B2 leads to minimum +20 for black in the end.
One of the perfect solutions:
Below you will find one perfect solution of the game.