The probability is 2/626, or 1/313 if you need to simplify.
Explanation:
Since a cube has 66 sides, and she wants to roll either a 11 or 22, she has two favorable outcomes. Her chances are is 22 out of 66 outcomes (to roll either a 11 or 22).
2/626 outcomes is equal to a 1/313 chance of a favorable outcome.