Final answer:
The sentence is a compound-complex sentence because it contains two main clauses connected by a conjunction, and one subordinate clause, making option (b) Complex sentence the correct answer.
Step-by-step explanation:
The sentence in question is: "While she was running around the shop, my mother realized she had left her wallet at home, and she had no money with her." To identify the type of sentence, we need to look at the structure and clauses within it. This sentence contains two main clauses: "my mother realized she had left her wallet at home" and "she had no money with her," which are connected by the conjunction 'and'. Additionally, there is a subordinate clause: "While she was running around the shop," which cannot stand alone as a complete sentence. Given this structure, the sentence is a compound-complex sentence because it has at least two main clauses and at least one subordinate clause. This sentence is not a simple sentence, a compound sentence, nor a run-on sentence. Therefore, the correct answer is: b) Complex sentence.