Find two consecutive even integers such that their sum is equal to the difference of three times the larger and two times the smaller.

Let first consecutive integer is X and other is X+2
as per given conditions
x+x+2=3 (x+2) - 2x
2x+2=3x+6-2x
2x+2=X+6
X=4
First even consecutive is 4 and other is 6