The sum of three consecutive even integers is less than 84. find the set of these three integers with the greatest sum.

Let the 3 numbers be x, x+2 and x+4, then

x + x + 2 + x + 4 < 84
3x + 6 < 84
3x < 84-6 
3x < 78
x <  26

so highest possible value of x is 24  so lets  add up the 3 numbers to
check if the sum is < 84

we have 24 + 26 + 28 =  78 

so answer is 24, 26 and 28.