Okay, so let us say that you possess 100g of compound: oxygen is 16.99 grams of it, so this means that we have 16.99 g / 16 g/mol which is equal to 1.062 moles of oxygen.
Considering that you had 16.99 grams of oxygen, then you have: 100 – 16.99 = 83.01 grams of M. We also know that it is two moles per M of oxygen based from the formula. That would mean that you have: 2 x 1.062 moles of M = 2.124 moles of M.
From this, we can conclude that the atomic weight of M is 83.01 / 2.124 = 39.09. The atomic weight that is closest to 39.09 is Potassium.
Therefore, the identity of M is K.