When evaluating the acidic properties of compounds, we must consider the nature of the oxides formed by different elements. The acidity of an oxide depends on the position of the respective element in the periodic table, particularly their electronegativity and the period to which they belong.

Oxides can be broadly categorized into four types based on the nature of the elements forming them:

Metallic oxides (usually basic)
Non-metallic oxides (usually acidic)
Amphoteric oxides (show both acidic and basic behavior)
Neutral oxides (do not show acidic or basic behavior)

Let's analyze the given compounds:

ZnO: Zinc oxide is amphoteric. It reacts with both acids and bases, but tends more towards basic than acidic properties.
Na₂O₂: Sodium peroxide is generally a basic oxide, but it can also react with water to form hydroxide ions, indicating it is less acidic than ZnO.
MgO: Magnesium oxide is a basic oxide. It reacts with acids to form salts and water but does not react with bases.
P₂O₅: Diphosphorus pentoxide is strongly acidic. It reacts readily with water to form phosphoric acid.

Based on the typical behavior of their chemical classification, here is the order of increasing acidic property:

Na₂O₂ (mostly basic)
MgO (basic)
ZnO (amphoteric, weakly acidic)
P₂O₅ (strongly acidic)

The increasing acidic behavior aligns with moving from basic, through amphoteric, to strongly acidic oxides.