Answer:
33, 34
Explanation:
the problem statement is competent confusing. is that really what your teacher asked you ?
adding two even integer numbers (it did not matter which ones) always result in an even number.
67 is uneven.
so it cannot be the result of 2 even numbers. "consecutive" or not. let alone the fact that 2 even numbers cannot actually be consecutive, because there is always an uneven number after each even number. but with some eyes closed one can understand that this could have meant "an even number and the next even number after that". but still, my first point is a real blocker.
so, I decided to ignore "even" and went for "two consecutive numbers".
x + (x+1) = 67
2x + 1 = 67
2x = 66
x = 33
x+1 = 34