Relation between number of equivalents of reactants
Step 1: Balance the equation. Your equation as written $\ce{ Sb2S3 + F2 -&gt; SbF5 + SF6}$ is not balanced. You do not have the same numbers of sulfur, antimony, or fluorine atoms on each side of the equation. You cannot say anything about equivalents or stoichiometry with an unbalanced equation. Hint: Start with $\ce{Sb}$ and $\ce{S}$ and balance $\ce{F}$ last.

Step 2: Determine the relationship between $x$ and $y$. Since $x$ is antimony and $y$ is sulfur and they are in the same compound initially, they have a relationship (but they are not equal). In $\ce{Sb2S3}$, there are 2 sulfur atoms for every 3 antimony atoms. What does that tell you that the ratio of $\frac{x}{y}$ must be?

Step 3: Use what you now know about $x$ and $y$ and the correct stoichiometric equivalents (which should give you $z$) to show that $x+y=z$.