the three consecutive even integers can be written as:

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

three times the first equals the sum of the other two:

3(2x - 2) = 2x + (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 even integer are 6, 8 and 10.