Since opposite sides of a standard six-sided die always add up to 7, we know that the side opposite the 3-dot side must have 4 dots, and the side opposite the 5-dot side must have 2 dots.
Since Nelson is covering the opposite sides with his fingers, the sides with 4 and 2 dots must be the ones under his fingers. Therefore, there are a total of 4 + 2 = 6 dots on the sides under his fingers.