Let the integers be x, y and z.

Given that the sum of the three integers is 66.

==> x + y + z = 66..............(1)

Also, given that the second integer (y) is 2 more than the first (x).

==> y = x + 2 ..................(2)

Also, given that the third (z) is 4 more than 2 times the first (x).

==> z = 2x + 4 ...........(3)

Now we will substitute (2) and (3) into (1).

==> x + y + z = 66

==> x + (x+2) + (2x+4) = 66

Now we will combine like terms.

==> 4x + 6 = 66

Subtract 6 from both sides.

==> 4x = 60

==> x = 60/4 = 15

==> y= x+2 = 15+2 = 17

==> z = 2x+4 = 2*15 + 4 = 30+4 = 34

Then the three integers are 15, 17, and 34