Four times the first of three consecutive even integers is six more than the product of two and the third integer. find the integers.

Assume the first integer is x, then the rest two are x+2, x+4

So 4x - 6 = (x+2)(x+4)

-> 4x - 6 = x^2 + 6x + 8

-> x^2 + 2x + 14 = 0

Not sure if there are problems with your question description, but apparently no real solutions are possible here.