Final answer:
The combination producing a short offspring with black hair would need the tt genotype for height and at least one B allele for hair color, which results in either ttBb or ttBB. Without the actual Punnett square provided, we cannot determine the exact possibility that corresponds to this combination.
Step-by-step explanation:
To determine which possibility would produce a short offspring with black hair, we need to look at combinations of two traits: height (T for tall, t for short) and hair color (B for black hair, b for red hair). Since the problem states that a person with the T gene will be tall and a person with the t gene will be short, and also that a person with the B gene will have black hair and a person with the b gene will have red hair, we are looking for a ttBb or ttbb combination, as 'tt' denotes shortness, and 'Bb' or 'bb' would give black hair due to 'B' being dominant (if present) or red hair if only 'bb' is present.
Without the actual Punnett square provided in the question, it's not possible to determine which possibility (A, B, C, or D) directly corresponds to the genotype producing a short offspring with black hair. However, based on the information given, we can infer that the only combination that results in a short offspring with black hair would have to include a 'tt' genotype as well as at least one 'B' allele if other options include it (ttBb or ttBB), but it could be 'ttbb' if black hair is not a factor in the offspring being considered.