Determining Rate Law and Reaction Mechanism from Method of Initial Rates
Empirical rate law is:

$$\mathrm{Rate} = \frac{[\ce{A}][\ce{B}]}{[\ce{B}] + [\ce{C}]}$$

In the first block of data you can notice that $\ce{C}$ and $\ce{D}$ are not necessarily required for reaction to proceed because otherwise the rate would be zero. You can also deduce that their concentration must appear as a sum in the rate law for the same reason. The sum will appear in denominator because $\ce{C}$ slows down the overall reaction.

Next step is to guess elementary reactions. From the law's denominator sum you can conclude that intermediate will competitively react with $\ce{B}$ and $\ce{C}$. 

$\ce{A -&gt;[k1] I}$ (Probably some kind of excitation)  

$\ce{I + C -&gt;[k2] D}$  

$\ce{I + B -&gt;[k3]Product}$

Then you derive the overall rate via steady state approximation (assumption).

$$\mathrm{Rate} = \frac{k_1k_3[\ce{A}][\ce{B}]}{k_3[\ce{B}] + k_2[\ce{C}]}$$

and ${k_1}={k_2}={k_3}$