The shape looks like a box with a chunk taken out of it. So, to find the volume of the shape, let us find the volume of the hypothetical "perfect" box and then subtract the volume of the chunk.
Volume of the box = 15x6x12 = 1080 cm³
Volume of the chunk = 10x6x4 = 240 cm³
Volume of weird shape = 1080-240 = 840 cm³
Answer: 840 cm³