Final answer:
The specific identification method of calculating basis provides the greatest opportunity for minimizing taxable gains or enhancing losses when selling stocks, by selecting individual lots of shares with the highest cost basis for sale.
Step-by-step explanation:
When selling stocks, the method of calculating basis that provides the greatest opportunity for minimizing gains or increasing losses is specific identification. This method allows the seller to choose which shares to sell based on their individual cost basis. For example, if a seller has multiple lots of the same stock purchased at different times and prices, they can select the lot with the highest purchase price for sale to minimize gain or maximize a loss for tax purposes. Alternatives such as LIFO (Last-In, First-Out), FIFO (First-In, First-Out), and weighted average do not offer the same level of control because they are subject to predefined rules on which shares are considered sold.