Answer
+6
Work Step by Step
Barium Sulfate, BaSO4. Barium is an alkaline earth metal so it is always +2. Oxygen is usually -2 (except in peroxide, which this is not). This means we have +2 from the barium and 4*-2 = -8 from the oxygens. Since the element is uncharged, it means that it must have a net charge of 0. This means we have 0 = 2 - 8 + oxidation number Sulfur.
This means that
Oxidation Number Sulfur = -2+8 = +6