Given that every single black stone is in atari, some strange things will have to happen if black is to capture everything. Luckily, half of the 4x4 board is made of 1-2-points, where such things are known to happen :-)
This is problem 42 from a Japanese booklet "Cho U's world of four roads 1", which comes with Nihon Ki-in's Monthly Go World magazine's issue 1/2011.