1. For a reaction with rate law $\text{rate} = k [\text{conc.}]^n$ taking logarithm gives: $\log(\text{rate}) = \log k + n\log(\text{conc.})$

2. Thus, in a plot of $\log(\text{rate})$ vs. $\log(\text{conc.})$:

   • the slope of the line = order of reaction.

3. Therefore, to compare the orders $a,b,c,d$, we only need to compare the slopes of the four lines corresponding to reactions:

   • $A \to P_1$ has order $a$
   • $B \to P_2$ has order $b$
   • $C \to P_3$ has order $c$
   • $D \to P_4$ has order $d$

4. From the given graph, the line for reaction $D$ has the greatest slope, followed by $B$, then $A$, and finally $C$ with the least slope.

5. Hence, $d > b > a > c$

6. Comparing with the options:

   • Option A: $d > b > a > c$ ✅
   • Option B: $d > a > b > c$ ❌
   • Option C: $a > b > c > d$ ❌
   • Option D: $c > a > b > d$ ❌

Therefore, the correct answer is Option A.