How to calculate the rate of formation of a product when given the rate law?
$$r=k \times [NO_2]^2 \times [Cl_2]$$

From the initial condition information =>
$$k=\frac{r}{[NO_2]^2 \times [Cl_2]}$$
Plugging the numbers=>
$$k=\frac{1.43 \times 10^{-6}}{0.25^2 \times 0.25}$$
So, $$k=9.152 \times 10^{-5}$$
For 0.11 condition =>
$$r=9.152 \times 10^{-5} \times 0.11^2 \times 0.11$$
or $$r=1.21 \times 10^{-7}$$