Question 741767
Let x = 1st consecutive even integer
Then, x + 2 = 2nd consecutive even integer
And, x + 4 = 3rd consecutive even integer

Now, we build our equation based on the words given to us.

4(x + x + 4) = 6(x + 2) - 8

The part on the left is 4 times the sum of the first and third integer
The part on the right is 8 less than 6 times the sum of the second integer

Now, we just need to remove parenthesis, collect like terms and solve for x.
This "x" will give us the first integer and putting it back into the other expressions given for the 2nd and 3rd integers will give us those.

4(x + x + 4) = 6(x + 2) - 8
4(2x + 4) = 6(x + 2) - 8       Collect like terms on the left side
8x + 16 = 6x + 12 - 8          Remove parenthesis by distributing
8x + 16 = 6x + 4               Collect like terms on the right side
8x - 6x = 4 - 16               Collect like terms: variables on left side and  numbers without variables on the right side

2x = -12                        Divide both sides by 2
x = -6   This is the first integer
x + 2 = -6 + 2 = -4   This is the second integer
x + 4 = -6 + 4 = -2   This is the third integer