Answer:
Yes ,The base neutralize all of the acid because it(base) is present in excess quantity .
Mg(OH)2 is in excess by 0.205 mole
Step-by-step explanation:
The balanced equation is :

Calculate the moles of Hydrochloric Acid and Magnesium hydroxide
For HCl

Given mass = 20.0 g
Molar mass of HCl = 36.5 g/mol

mole of HCl = 0.55
For Mg(OH)2
Given mass = 28.0 g
Molar mass of Mg(OH)2 = 58.3 g/mol

mole of Mg(OH)2 = 0.48
According to the balanced equation ,

1 mole of Mg(OH)2 would require = 2 mole of HCl for neutralisation
So,
0.48 mole of Mg(OH)2 would require = 2(0.48) = 0.96 mol
HCl needed for complete neutralisation = 0.96 mole
Available HCl = 0.55 mole
HCl is less by = 0.96 -0.55 = 0.41 mole
So,
Mg(OH)2 is in excess by = 0.41/2 mole [because 1 HCl = 2 Mg(OH)2]
= 0.205
Here HCl is less than need and Mg(OH)2 is in excess.