Because chemical equations CONSERVE mass; #"garbage in must equal garbage out"#. This mass balance has been ABSOLUTELY confirmed in every chemical reaction ever performed.
And since there are 3 moles of oxygen on the right hand side (RHS) of the equation, there must be 3 moles of oxygen on the LHS:
#ZnS +3/2O_2 rarr ZnO + SO_2#
If you dislike the 1/2 integral coefficient, on the LHS, you can simply double the entire equation:
#2ZnS + 3O_2 rarr 2ZnO + 2SO_2#
Is this balanced? It must be if it represents a VALID chemical reaction.
Note that you do this sort of thing, this assessment of stoichiometry, ALL the time. If you buy an item for #£4-50# in a shop with a #£10-00# note, would you buy satisfied if the shopkeeper gave you #£3-50# in change? I don't think you would, and here you make precisely the assessment of balance, of stoichiometry, as we did in the prior equation. Because here you use money, you are trained to notice this sort thing IMMEDIATELY. I maintain that you can make the same judgement of chemical reactions automatically, and that you can balance symbol equations quickly and straightforwardly.
See here for more details, and here for an example regarding combustion.