The correct answer is B. Dr. Mitchell is my family physician, and his office is near my home.
Explanation:
A compound sentence is a type of sentence that includes two or more independent clauses which are units with complete meaning and that do not need other sentences. In terms of punctuation, these sentences can be linked using a semicolon between the independent clauses or a comma followed by a coordinating conjunction (and, or, so, but). This implies, the sentence that is a compound sentence and has correct punctuation is option B because this contains two independent clauses "Dr. Mitchell is my family physician" and "his office is near my home" and these have been linked using a colon followed by one of the coordinating conjunctions which is correct. Also, other options are not compound sentences or do not use punctuation correctly.