The product of two positive consecutive even integers is 6 more than three times their sum. find the product of the integers.

Let the integers be x and x + 2, provided x is an even value.

The product is six more than 3 times their sum.

x (x + 2) = 6 + 3 (x + (x + 2))

By expanding and simplifying, we get:

x² + 2x = 6 + 3 (2x + 2)

x² + 2x = 6 + 6x + 6

x² + 2x = 12 + 6x

x² - 4x - 12 = 0

(x - 6) (x + 2) = 0

x = 6 or x = - 2.

Thus, your integers are: 6 and 8 or - 2 and 0