The total distance swimmer finished is 6400 meters. The distance travlled in 400 meter races and 200 meter races is equal to total diatance. So equation for x number of 200 meter races is,
[tex]\begin{gathered} 12\cdot400+x\cdot200=6400 \\ 200x=6400-4800 \\ x=\frac{1600}{200} \\ =8 \end{gathered}[/tex]So there are 8 number of 200 meter races.