The method used for balance ${\mathrm{S}}_3+{\mathrm{O}}_2\to {\mathrm{SO}}_3$ is [[1]] or inspection method.

The chemical formula of the reactant and the chemical formula of the product make up a chemical equation. Each particular substance's chemical formula is distinguished from others by a plus sign, and the two are divided by an arrow symbol.

Each side of the chemical equation in a balanced equation must represent the same amount of each element. The same charge must consequently be present on both sides of a balanced chemical equation, according to the rule of conservation of mass.
By altering the scalar value for each chemical formula, one might balance a chemical equation. By using trial and error or a set of linear equations, it is possible to balance simple chemical equations.
(1) Placing coefficient 1 in front of the most complicated formula and the other coefficient in front of everything else so that each atom is present on both sides in some quantity.
(2) Multiply each coefficient by the smallest number necessary to bring them all to a whole, which is often the fractional coefficient for a reaction with a single fractional coefficient.
We must balance the chemical reaction that results from,

Trial error or inspection method is used for the balancing the equation ${\mathrm{S}}_8 + {\mathrm{O}}_2\to {\mathrm{SO}}_3$.

The equation formed after balancing the given equation is: ${\mathrm{S}}_8+12{\mathrm{O}}_2\to 8{\mathrm{SO}}_3$.

Hence, the answer is Trial error .