Learn Russian: Они шли сквозь лес и долго обходили лужи и грязь. - They were walking through the forest and went around puddles and mud for a long time.

The adverb долго (for a long time) shows this was an ongoing, continuous process, which requires the imperfective aspect. They were constantly navigating around obstacles as they walked, rather than just completing the action of bypassing a single puddle once.

What case do the words лужи and грязь take after обходили?

They are in the Accusative case because verbs of motion with the prefix об- or обо- (meaning to go around, bypass, or avoid) become transitive. This means they take a direct object in the Accusative case without needing an extra preposition.

Both сквозь and через mean "through". Why is сквозь used here?

While через is a neutral word for crossing a space, сквозь specifically implies pushing through something dense, thick, or with some resistance. Using сквозь лес paints a picture of a thick, overgrown forest rather than an open, easy trail. Both prepositions take the Accusative case.

Why does the sentence start with the unidirectional verb шли if they are weaving around puddles?