How many isomers does a compound with molecular formula C2BrClFI give?

The general structure of the compound, disregarding isomers, consists of a C=C double bond with two halogens attached to one of the carbons and two attached to the other. Now pick one of the halogens, say F. Note that it can be paired with Cl, Br, or I on the same carbon atom and that the choice of its partner means the other two halogens must be placed on the other carbon atom. So there are 3 structural isomers that we can draw. For each of these structural isomers, there are two geometric isomers that we can draw depending on whether the highest priority atoms are on the same side or on opposite sides (priority being determined by the atomic number of the element). Thus, there are altogether 2 x 3 = 6 isomers of the compound in question. This reasoning is the equivalent of actually drawing out all the possible isomers. However, with this method we've been able to avoid drawing duplicate structures which are interchangeable by rotation, reflection, or inversion.