My algebra text writes for the number of cyclic structures (-,-)(-,-) in $S_4$
$\frac{{4\choose 2}\cdot {2 \choose 2}} {2}$
which should be {(1 2)(3 4), (1 3)(2 4), (1 4) (2 3)}.
The binomial coefficient part "$C_{4,2} \cdot C_{2,2}$" should mean select 2 objects out 4 for the first cycle and 2 out the remaining 2 for the second cycle. I don't understand what dividing by 2 accomplishes, the author does not provide any information about it. I'd like to understand it from a combinatorics point of view, and be able to generalize to $S_n$.
So far I've understood that the length of a r-cycle is n!/r(n − r)!. But I'm unsure how to pass from r-cycles to product of r-cycles.