Answer
Kp = 3.423
Work Step by Step
We are interested in Kp for the reaction
2SO$_2$ + O$_2$ 2SO$_3$
Which is 2 times the original reaction. Since both the reactants and the products now have double their original stoichiometric coefficients, this will result in the original expression of Kp being squared (since the concentrations are raised to their coefficients in the expression for Kp).
Therefore, if the original Kp is 1.85, the new Kp would be 1.85 squared, which is 3.423.
