Answer
$SO_2$ and $SO_3$: $\frac{2 \space moles \space SO_2}{2 \space moles \space SO_3}$ and $\frac{2 \space moles \space SO_3}{2 \space moles \space SO_2}$
$SO_2$ and $O_2$: $\frac{2 \space moles \space SO_2}{1 \space mole \space O_2}$ and $\frac{1 \space mole \space O_2}{2 \space moles \space SO_2}$
$O_2$ and $SO_3$: $\frac{1 \space mole \space O_2}{2 \space moles \space SO_3}$ and $\frac{2 \space moles \space SO_3}{1 \space mole \space O_2}$
Work Step by Step
1. Use the balance coefficients to write the mole-mole equalities:
2 moles $SO_2$ = 2 moles $SO_3$
2 moles $SO_2$ = 1 mole $O_2$
1 mole $O_2$ = 2 moles $SO_3$
2. Use these equalities to write the conversion factors:
$\frac{2 \space moles \space SO_2}{2 \space moles \space SO_3}$ and $\frac{2 \space moles \space SO_3}{2 \space moles \space SO_2}$
$\frac{2 \space moles \space SO_2}{1 \space mole \space O_2}$ and $\frac{1 \space mole \space O_2}{2 \space moles \space SO_2}$
$\frac{1 \space mole \space O_2}{2 \space moles \space SO_3}$ and $\frac{2 \space moles \space SO_3}{1 \space mole \space O_2}$
