$2(+1)+2 x+7(-2)=0$

$x=+6$

In $K _{2} Cr _{2} O _{7},$ Transition metal $( Cr )$ present in +6

oxidation state.

$KMnO _{4}$

$(+1)+y+4(-2)=0$

$x=+7$

In $KMnO _{4}$, transition metal (Mn) present in $+7$ oxidation state

$K _{2} FeO _{4}$

$2(+1)+z+4(-2)=0$

$x=+6$

In $K _{2} FeO _{4},$ transition metal (Fe) present in $+6$ oxidation state

So $x=+6$

      $y=+7$

      $z=+6$

____________

$x+y+z=19$