18.0 grams of oxygen is reacted with nitrogen to make 56.0 grams of nitrogen dioxide according to the following reaction:
2O2 + N2 ---> 2 NO2
How much nitrogen (in grams) reacted?

You say you obtain a total of 56 g of NO2. What does this product consist of? How many grams of each component must be in the product to produce 56 grams?

Another way to look at it:
From your equation, 2 mol of O2 and 1 mol of N2 react to form 2 mol of NO2

Remember that 1 mol of a substance has a mass equal to the relative mass of the atoms in that substance..

To add to my first answer: do you see that you CANNOT get 56 grams of NO2 starting with 18 grams of O2?