let the three consecutive even positive integers can be written as

2x -2, 2x and 2x + 2

where x is integer and 2x - 2 < 2x < 2x + 2

the product of the two smaller integers is 28 more than twice the largest

(2x - 2)2x = 28 + 2(2x + 2)

by solving we find

x = 4

click here to see the step by step solution of the equation

2*4 - 2 = 6

2*4 = 8

2*4 + 2 = 10

the three consecutive positive even integers are 6, 8 and 10.