Negative Times Positive

Multiplying by a whole number is repeated addition: $3\cdot 5$ is three 5s. That works for a negative number too. $\left(-4\right) \cdot 3$ is three -4s added together, $-4 + \left(-4\right) + \left(-4\right)$, which is -12.

On the number line, that is three jumps of 4 to the left, ending at -12. In money: owing 4 dollars to each of three friends means you owe 12 in all. The size is the ordinary product, 4 times 3, and the sign is negative.

The order of the factors still does not matter, so $3 \cdot \left(-4\right)$ is -12 as well. A negative times a positive is negative, whichever comes first.