4times the lesser of two consecutive even integers is 12 less than twice the greater number. find the integers

Let the two consecutive even integers be 2n + 2n + 2.

4 times the lesser of the two integers is 12 less than twice the greater number. Therefore
4(2n) = 2(2n + 2) - 12
8n = 4n + 4 - 12
4n = -8
n = -2

Therefore
2n = -4
2n + 2 = -2

The integers are -4 and -2.