The given equation can be balanced using ion-electron method as shown below.
Fe2+→Fe3++e− -oxidation Half reaction
6e−+14H++Cr2O72−→2Cr3++7H2O -Reduction Half reaction
The overall reaction is
6Fe2++14H++Cr2O72−→6Fe3++2Cr3++7H2O
The values X=14,Y=2andZ=7
(X+Y+Z)=14+2+7
=23