To find the moles of oxygen, you need to (1) convert grams Mn(ClO₄)₄ to moles Mn(ClO₄)₄ (via molar mass) and then (2) convert moles Mn(ClO₄)₄ to moles O (via mole-to-mole ratio from formula subscripts). It is important to arrange the conversions/ratios in a way that allows for the cancellation of units.
Molar Mass (Mn(ClO₄)₄): 452.74 g/mol
1 Mn(ClO₄)₄ = 1 Mn and 4 Cl and 16 O
175.7 g Mn(ClO₄)₄ 1 mole 16 moles O --------------------------- x ------------------- x --------------------------- = 6.21 moles O 452.74 g 1 mole Mn(ClO₄)₄