Part B is incorrect. The phrase "heavy trodden" is grammatically incorrect because "heavy" is an adjective, but the sentence requires an adverb to modify the verb "trodden" (the third form of "tread"). When modifying a verb or past participle, an adverb should be used instead of an adjective. Here, "heavily" (adverb) correctly describes how the road is trodden. The correct form should be "heavily trodden" instead of "heavy trodden".
Parts A, C, and D are correct.
The correct sentence is: Day after day, the road is heavily trodden by thousands of pedestrians who walk to work and back home.
Hence, option (b) is correct.