The chemical formula of Chromyl chloride is ${\mathrm{CrO}}_2{\mathrm{Cl}}_2$. The oxidation state of chromium in chromyl chloride (${\mathrm{CrO}}_2{\mathrm{Cl}}_2$) is $+6$.

Let the oxidation number of Chromium be “$\mathrm{x}$”, the oxidation state of oxygen  is $-2$, the oxidation state of chlorine  is $-1.$

Then,

 $\mathrm{x} + 2(-2) + 2(-1) = 0$

$$\begin{gathered} \mathrm{x}-6=0 \\ \mathrm{x}=6 \end{gathered}$$