The answer is 16, 18, 20
Let the number be x, the the three consecutive even integers are x, x+2, and x+4; then the sum is 3x+6.
We the can form a equation from the sentence “the sum is 10 less than 4 times of the smallest number”:
3x+6+10 = 4x
3x+16 = 4x
x = 16
Then, we obtain
x+2 = 16+2 = 18
x+4 = 16+4 = 20
Thus, the three consecutive even integers are 16, 18, 20.