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