Gasoline dissolves Styrofoam through a chemical reaction with the Styrofoam and the gasoline.
Styrofoam is a trade name for polystyrene (PS) foams.
Polystyrene readily dissolves in many various kinds of organic substances, such as, but not limited to, acetone, MEK, THF, benzine, hexane, and hexene, plus heavier hydrocarbons.
Gasoline is a mix of hydrocarbons, so it dissolves PS, producing a viscose paste.
The resulting, sticky and gelatinous material, is effectively home made “napalm”.
It can be be made by dissolving pieces of Styrofoam in gasoline or diesel fuel to form a flammable jelly-like substance.
Napalm is an aluminum soap used to prepare incendiary mixtures composed by the gelling agent and a compatible volatile petrochemical (usually gasoline (petrol), kerosene and diesel fuel).
Any thickened fuel is often referred to as napalm, even though it doesn't contain aluminum salts.
Since polystyrene only contains carbon hydrogen bonds, it is nonpolar and will only dissolve in nonpolar solvents, because like dissolves like.
This is why the non-polar polystyrene dissolves in acetone or gasoline but not water and the polar starch molecules dissolve in water but not acetone.