The chemical reaction described by the question:

Then for finding the number of moles of magnesium hydroxide Mg(OH)

number of moles = mass (grams) / molecular mass (g/mole)
number of moles of Mg(OH)
= 355 / 58 = 6.12
From the chemical reaction:
1 mole of Mg(OH)
reacts with 2 moles of HCl
6.12 moles of Mg(OH)
reacts with x moles of HCl
x = (6.12×2)/1 = 12.24 moles of HCl
And now we can determine the mass of hydrochloric acid HCl
mass (grams) = number of moles x molecular mass (grams/mole)
mass of HCl = 12.24 × 36.5 = 446.76 g