1) First error is chemical formula of zinc hydroxide. Correct formula for this compound is Zn(OH)₂, because zinc has oxidation number +2 and hydroxide anion has negative charge -1.
Second error is molar mass of zinc hydroxide.
M(Zn(OH)₂) = Ar(Zn) + 2Ar(O) + 2Ar(H) · g/mol.
M(Zn(OH)₂) = 65.38 + 2 · 16 + 2 · 1.01 · g/mol.
M(Zn(OH)₂) = 99.4 g/mol; molar mass of zinc hydroxide.
2) Third error is the unit, unit for molar mass is g/mol (gram per mole), not mol.
Fourth error is formula for calcutating amount of zinc hydroxide.
It should be done like this:
m(Zn(OH)₂) = 0.45 g; mass of zinc hydroxide.
M(Zn(OH)₂) = 92.4 g/mol.
n(Zn(OH)₂) = m(Zn(OH)₂) ÷ M(Zn(OH)₂).
n(Zn(OH)₂) = 0.45 g ÷ 92.4 g/mol.
n(Zn(OH)₂) = 0.0048 mol; amount of zinc hydroxide.
There is not need to multiply with Avogadro consta (6.022·10²³ 1/mol).