let note x the first even integer, the second which is consecutive is x+2 and the third x+4, so the equation to solve is x + x+2 + x+4 = 54 so 3x +6 = 54 then 3x = 48 and x = 16,

The first integer is 16, the second 18 and the third 20, you can see that 16 +18 + 20 = 54