The difference between two consecutive integers is 2.
Let n be the smallest of the three even integers.
Then the next larger even integer is n + 2.
The largest even integer is n + 4.
Now we follow what the problem tells us.
Twice the smallest is 2n
3 times the larges is 3(n + 4)
2n + 3(n + 4) = 42
2n + 3n + 12 = 42
5n + 12 = 42
5n = 30
n = 6
n + 2 = 8
n + 4 = 10
The integers are 6, 8, 10