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
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