The correct option is B Her shoes were old and worn out, yet they looked sturdy and of good quality.
A compound sentence is made up of two independent clauses, which are
complete sentences on their own. Adversative compound sentences contain
two ideas that contrast each other in meaning. The conjunctions used in
such sentences include but, yet, still and so on.
Option B contains the adversative conjunction 'yet', which means 'in spite of that'. It refers to the contrast between the clauses ("old and worn out" vs "sturdy and of good quality"). Hence B is correct.
Option A uses the illative conjunction 'so', which is used in inference-related sentences. The original sentence does not express any inference, hence A is incorrect.
Option C uses a participial phrase, "being...," and not an adversative conjunction. The resulting sentence is not an adversative compound sentence. Hence C is incorrect.
Option D is incorrect as the answer lies in B.