A gas reaction has the rate law rate = k[A]²[B]…

(a) Order and unit. The overall order is $2 + 1 = 3$. For order 3, the unit of $k$ is $\text{L}^2\ \text{mol}^{-2}\ \text{min}^{-1}$ with the time in minutes.

(b) The value. We want $k$, so $k = \dfrac{\text{rate}}{[\text{A}]^2[\text{B}]}$.

$k = \dfrac{6.0 \times 10^{-4}\ \text{mol L}^{-1}\ \text{min}^{-1}}{(0.20\ \text{mol/L})^2 \times 0.50\ \text{mol/L}} = \dfrac{6.0 \times 10^{-4}\ \text{mol L}^{-1}\ \text{min}^{-1}}{0.020\ \text{mol}^3\ \text{L}^{-3}} = 0.030\ \text{L}^2\ \text{mol}^{-2}\ \text{min}^{-1}$.