Show that there are just three members of $S_4$ which have two cycles of length 2 when written in cycle notation.
I'm having trouble figuring out how I should test this. It seems dumb to write out all 24 permutation combinations and then convert them to cycle notation.
Assuming (and we can. Why?) the cycles are pairwise disjoint, it is clear the only such elements are $\;(12)(34),\,(13)(24),\,(14)(23)\;$ .