To determine the number of compounds with a +4 oxidation state of sulfur, we need to examine the oxidation states of sulfur in each of the listed compounds. The +4 oxidation state means that sulfur has lost 4 electrons compared to its elemental state.

Let's go through each compound:

• $$\mathrm{SO}_3$$: Sulfur trioxide. In this compound, sulfur exhibits a +6 oxidation state because each oxygen contributes -2, for a total of -6 (3 oxygens), which must be balanced by sulfur to maintain a neutral charge. So, this compound does not have sulfur in the +4 oxidation state.


• $$\mathrm{H}_2 \mathrm{SO}_3$$: Sulfurous acid. Here again, with two hydrogens (each contributing +1 = total +2) and three oxygens (each contributing -2 = total -6), sulfur has an oxidation state of +4 to balance out the -4 from the oxygens and +2 from the hydrogens. This compound does have sulfur in the +4 oxidation state.


• $$\mathrm{SOCl}_2$$: Thionyl chloride. Sulfur in this compound is connected to two chlorine atoms and one oxygen atom. Chlorine generally has an oxidation state of -1 (total -2 for both Cl atoms) and oxygen -2. To balance the -4 charge (from one oxygen and two chlorines), sulfur must have an oxidation state of +4. This compound has sulfur in the +4 oxidation state.


• $$\mathrm{SF}_4$$: Sulfur tetrafluoride. Fluorine is almost always in the -1 oxidation state, and there are four fluorine atoms for a total of -4. To balance this, sulfur must have a +4 oxidation state, making this compound one with sulfur in the +4 oxidation state.


• $$\mathrm{BaSO}_4$$: Barium sulfate. Barium has a +2 oxidation state, and sulfate (SO4) as a whole must have a -2 oxidation state to balance the barium. In sulfate, sulfur has an oxidation state of +6 (since each oxygen is -2 for a total of -8, and +6 from sulfur balances it to -2 overall). Hence, sulfur does not have a +4 oxidation state in this compound.


• $$\mathrm{H}_2 \mathrm{S}_2 \mathrm{O}_7$$: Pyrosulfuric acid or oleum. Each hydrogen is +1 (total +2), and the seven oxygens are -2 each (total -14). To balance -12 (total of oxygens and hydrogens), each sulfur must have an oxidation state of +6. Therefore, sulfur is not in the +4 oxidation state in this molecule.

So, from the given list, only three compounds have sulfur in the +4 oxidation state: $$\mathrm{H}_2 \mathrm{SO}_3$$, $$\mathrm{SOCl}_2$$, and $$\mathrm{SF}_4$$. Therefore, the number of compounds with a +4 oxidation state of sulfur is three.