If Instantaneous rate of reaction is stated as $-\frac{1}{2} \frac{\mathrm{~d}[x]}{\mathrm{dt}}=-\frac{\mathrm{d}[\mathrm{y}]}{\mathrm{dt}}=\frac{1}{2} \frac{\mathrm{~d}[\mathrm{z}]}{\mathrm{dt}}$, identify the reaction.

The instantaneous rate expression provides direct insight into the reaction stoichiometry. For a general reaction $aA + bB \rightarrow cC + dD$, the rate is defined as $\text{Rate} = -\frac{1}{a} \frac{d[A]}{dt} = -\frac{1}{b} \frac{d[B]}{dt} = +\frac{1}{c} \frac{d[C]}{dt} = +\frac{1}{d} \frac{d[D]}{dt}$.

Given the rate expression $-\frac{1}{2} \frac{d[x]}{dt} = -\frac{d[y]}{dt} = \frac{1}{2} \frac{d[z]}{dt}$, the stoichiometric coefficients are determined by the denominators. The negative terms indicate reactants, while the positive term indicates a product.

The balanced reaction must be $2x + y \rightarrow 2z$, which corresponds to option B.