B

Step 1: For a one-eyed person, the size of the mirror required can be calculated using the height of the face and the distance from the eye to the bottom of the face.
The height of the person's face is 24 cm. For a one-eyed person, the mirror needs to be at least half the height of the face, so:

• Minimum size needed for reflection = \frac{24 ext{ cm}}{2} = 12 ext{ cm}

Step 2: The width required for a one-eyed person is equal to the width of the face, which is 16 cm.
Therefore, the total minimum size needed for the looking glass is 12 cm in height and 16 cm in width.
Step 3: For a two-eyed person, the size of the mirror required increases slightly since he will need to see a bit further outwards. The width remains the same (16 cm), but we need to consider the eye separation. So, the minimum width required = Width of the face + Separation between the eyes = 16 cm + 8 cm = 24 cm.
Step 4: For the height, the requirement remains the same, so it's still 12 cm.

In summary:

• One-eyed: 12 cm x 16 cm
• Two-eyed: 12 cm x 24 cm

Step 5: The smallest size of looking glass for a two-eyed person is therefore 12 cm x 24 cm. Hence, this would be the final answer.
Therefore, the answer is: B (12 cm x 24 cm).