find four consecutive even integers such that the sum of the third and fourth is 6 less than four times the first

The numbers are 2, 4, 6 and 8

Step-by-step explanation:

let the four numbers be x, y, z and l respectively

then:

x+y+z+l

(z+l) - 6=4x

since they are all four consecutive even integers

then y=x+2

z=y+2=x+4

l=z+2=x+6

since (z+l) - 6=4x

then ((x+4) + (x+6)) - 6=4x

2x+4=4x

4=4x-2x

4=2x

2=x