Final answer:
The fatty acid in question is correctly named using the alpha naming system as trans-3, trans-7-dodecadienoic acid, but when using numeric notation, the answer is d. trans-3, trans-7-12:2.
Step-by-step explanation:
The question concerns the nomenclature of a fatty acid with a specific structure, having 12 carbons and two trans double bonds. The double bonds are located between the third and fourth carbons, and between the seventh and eighth carbons from the carboxylic acid end, known as the alpha (α) end. Using the alpha naming system, the correct way to name this fatty acid takes into account both the position of the double bonds from the α end and the trans configuration of these bonds.
According to the alpha naming system, the positions are indicated first, followed by the descriptor 'trans' to indicate the configuration of the double bonds, and finally the total number of carbons and the total number of double bonds are stated at the end. Therefore, the name of this fatty acid would be trans-3, trans-7-dodecadienoic acid, where 'dodeca' indicates the 12 carbons and 'dienoic' indicates the presence of two double bonds. However, when using numeric notation as provided in the options, the correct option is d. trans-3, trans-7-12:2, which summarizes the structure of the fatty acid succinctly.