For a general reaction $aA \rightarrow bB$, the rate of the reaction is expressed by dividing the rate of disappearance of reactants or appearance of products by their respective stoichiometric coefficients: $\text{Rate} = -\frac{1}{a}\frac{d[A]}{dt} = +\frac{1}{b}\frac{d[B]}{dt}$ .

Applying this to the given reaction $3A \rightarrow 2B$: $\text{Rate} = -\frac{1}{3}\frac{d[A]}{dt} = +\frac{1}{2}\frac{d[B]}{dt}$

To find the value of $+\frac{d[B]}{dt}$, rearrange the equation by multiplying both sides by 2: $+\frac{d[B]}{dt} = -\frac{2}{3}\frac{d[A]}{dt}$.