On a standard six-faced die,the numbers of the opposite faces always add to seven,Dena rolls a pair of fair,standard six-faced dice.She then takes the product of four numbers ,the two numbers on the faces that are showing on top of the dice and the two numbers on the faces which are hidden on the top of the dice.What is the greatest possible productof these four numbers?

4 * 3 * 4 * 3 = ?

its 144

To find the greatest possible product of the four numbers, we first need to determine the values on the two faces showing on top of the dice and the values on the hidden faces.

Since opposite faces of a standard six-faced die always add up to seven, we can determine the possible values for the two faces showing on top of the dice:

Let's assume the first die shows a value of x. Then, the value on the opposite face of that die would be 7 - x.

Now, let's assume the second die shows a value of y. Then, the value on the opposite face of that die would be 7 - y.

The four numbers we need to consider are x, 7 - x, y, and 7 - y.

To find the greatest possible product, we need to find the highest values for x and y. The numbers on a standard die range from 1 to 6.

If we set x and y as high as possible, x and y would be 6. Therefore, the four numbers in this case would be 6, 1, 6, and 1.

Now, let's calculate the product of these four numbers:
6 * 1 * 6 * 1 = 36

So, the greatest possible product of these four numbers is 36.