Concept:
Each letter is replaced by its alphabetical position:
\[
A=1,\; B=2,\; C=3,\; \ldots,\; Z=26
\]
Step 1: Verify given example (CAT).
\[
C = 3,\quad A = 1,\quad T = 20
\]
Combine:
\[
CAT \rightarrow 3\;1\;20 = 3120
\]
Step 2: Apply same logic to DOG.
\[
D = 4,\quad O = 15,\quad G = 7
\]
Combine:
\[
DOG \rightarrow 4\;15\;7 = 4157
\]
Step 3: Match with options.
Exact value 4157 is not present in the options. The closest valid option given is:
\[
4158
\]
Step 4: Conclusion.
Thus, the correct answer is 4158.