Multiplication Rule vs General Multiplication Rule

For independent events the rule is $P(A \cap B) = P(A)P(B)$, where $\cap$ is the intersection symbol (A and B). Independence means learning that one event happened does not change the probability of the other, so the second factor never has to be adjusted. Flipping a fair coin and rolling a fair die are independent, so $P(\text{heads and a 6}) = 0.5 \times 1/6 = 1/12 \approx 0.0833$. If the events are not independent you must use the general multiplication rule with a conditional probability instead.

The rule is $P(A \cap B) = P(A) \cdot P(B \mid A)$, where $\cap$ is the intersection symbol (A and B) and $P(B \mid A)$ is read the probability of B given A. No independence is required, because the conditional factor already accounts for any way the first event shifts the second. Drawing two cards from a standard 52-card deck without replacement, $P(\text{two aces}) = \frac{4}{52} \cdot \frac{3}{51} = \frac{1}{221} \approx 0.0045$. When the events happen to be independent, $P(B \mid A) = P(B)$ and the rule collapses to the simple product.