Using two bytes per pixel in a color image. Up to 65,536 colors can be represented in the color palette. Most graphics formats provide 8-bit color or 24-bit color; however, graphics cards ...

and the basic architectures were equal, a 32-bit computer would work twice as fast internally as a 16-bit computer. In practice, 8-bit, 16-bit, 32-bit and 64-bit architectures are rarely identical ...

The 65,536 colours required need a bit depth of 16 bits. If the scenario stated 256 colours the bit depth would be 8, had it stated 16,777,216 then the bit depth would have been 24.