Answer
$$ \frac{\Delta [NO_2]}{\Delta t} =0.015 \space mol \space L^{-1} \space s^{-1}$$
Work Step by Step
$$Rate = - \frac{1}{4}\frac{\Delta [NO_2]}{\Delta t} = - \frac{1}{1} \frac{\Delta [O_2]}{\Delta t}$$
Multiplying both sides by -4:
$$ \frac{\Delta [NO_2]}{\Delta t} = 4 \times \frac{\Delta [O_2]}{\Delta t}$$
$$ \frac{\Delta [NO_2]}{\Delta t} = 4 \times (0.0037 \space mol \space L^{-1} \space s^{-1}) = 0.015 \space mol \space L^{-1} \space s^{-1}$$
