We need a bit of algebra for this one...
x, y (two integers, x is smaller)
x, x+2 (consecutive even integers, so we know y in terms of x)
(x + y) (sum x, y)
(3y - 2x) (difference of three times the larger, and two times the smaller)
hence we have an equation
x + y = 3y - 2x
=> 3x = 2y
substitute (x + 2) to get 3x = 2(x + 2)
=> 3x = 2x + 4
=> x = 4
We know next number is x + 2 so y = 6
Double-check our workings: two consecutive even numbers? yes! sum of the two is 10. three times the larger is 18. 2 times smaller is 8. difference = 10. All good!