Look at the balanced equation and see what the mole ratio is between Ca(OH)2 and NaOH.
It takes 1 mol Ca(OH)2 to produce 2 moles of NaOH.
2NaBr + Ca(OH)2 ==> CaBr2 + 2NaOH
So, now we must find the moles of NaOH represented by 52.9 g NaOH. Once we have that, we can determine the moles of Ca(OH)2 that was used to make that and then convert moles to grams.
moles NaOH produced = 52.9 g NaOH x 1 mol NaOH / 39.99 g = 1.32 moles NaOH
moles Ca(OH)2 needed = 1.32 mols NaOH x 1 mol Ca(OH)2 / 2 mols NaOH = 0.661 mols Ca(OH)2
Converting this to grams, we have...
0.661 mols Ca(OH)2 x 74.09 g Ca(OH)2 / mol = 49.0 g Ca(OH)2