In the experiment of rolling a fair die twice and tossing a coin if the results match, there are 42 possible outcomes. The initial die rolls yield 36 combinations (6 sides on the die, rolled twice). If the two rolls are the same, a coin toss introduces an additional 6 outcomes (heads or tails for each of the 6 matching die results). Thus, the total outcomes consist of 30 from different die rolls and 12 from matching rolls leading to coin tosses. The calculation confirms that the total is indeed 42 outcomes.