Final answer:
A conjecture about the product of a positive and a negative number is that the product will always be negative, which is consistent with the multiplication rules of signs.
Step-by-step explanation:
To answer the question regarding a conjecture about the product of a positive and a negative number: we can state that whenever a positive number is multiplied by a negative number, the product will always have a negative sign. This can be exemplified by considering the provided examples: (-3) x 2 = -6 and 4 x (-4) = -16. Both examples clearly show that a positive number multiplied by a negative number results in a negative product.
The concept is consistent with the rules of multiplication regarding signs, where the sign of the product is dependent on the signs of the numbers being multiplied. Similarly, this rule is also applicable when dividing numbers, as division can be seen as a form of multiplication with reciprocals. Hence, dividing a positive number by a negative number will also yield a negative result.