As we are being asked to solve for the middle of three consecutive even integers, let this be x. Then, the first even integer is x - 2, and the third even integer is x + 2.
Then, we are given that 5 times the second of three consecutive even integers is six more than twice the sum of the first and third integers.
Translating this into an equation, we have
5 * x = 6 + 2 * (x-2 + x+2)
5x = 6 + 2 * 2x
5x = 6 + 4x
5x - 4x = 6
1x = 6
x = 6
Check the answer; the middle even integer is 6, so the first even integer is 4 and the third is 8
Then, 5 times the second even integer is 5 * 6 = 30
6 + 2 * the sum of the first and third integers is
6 + 2 *(4 + 8) = 6 + 2 * 12 = 30
30 = 30, so it checks
