The answer depends on the starting mass of Mg, so let's assume you start an experiment with 0.243g of Mg. The mass of MgO would need to be 0.403g of MgO.
How can you figure this out? I'll explain...
Magnesium oxide is an ionic compound, so we need to understand that the Mg atoms will form +2 ions by losing 2 electrons and the oxygen atoms will form -2 ions by gaining two electrons. This is why Mg and O will combine in a 1:1 ratio.
The mass of 0.234g Mg would be 0.01mol of Mg (0.243/24.3), which must combine with 0.01mol of O to form the compound. Multiplying the molar mass of oxygen by 0.01 (15.999 x 0.01 = 0.16) provides the mass of O which must combine with the Mg.
The total mass of the compound will be the mass of Mg and the mass of O added together (0.243 + 0.16 = 0.403g).
It is possible to work out the ending mass of the MgO which would produce the MgO ratio of 1:1. You just need to convert mass of Mg to moles (mass Mg/24.3) and find the mass of oxygen that would be equal to this number of moles. Then add the two masses together.