Two consecutive even integers can be given as 2x and 2x+2 where x is some integer we will solve for. The smaller added to two times the larger is then given by 2x + 2(2x+2) = 2x + 4x + 4. Set this equal to 34 and we have 2x + 4x + 4 = 34. Subtract 4 from both sides and we have 6x = 30. Divide both sides by 6 and we have x = 5. Our numbers are 2x and 2x+2 so putting x = 5, we have that our numbers are 10 and 12.