Final answer:
The correct punctuation is option C. The sentence should be: I would like to take a vacation at the end of this month; however, it is a busy time of year at our office.
Step-by-step explanation:
The correct punctuation is option C. The sentence should be:
I would like to take a vacation at the end of this month; however, it is a busy time of year at our office.
The use of a semicolon (;) before the word 'however' is appropriate because it separates two independent clauses. The comma after 'however' is necessary to set apart the transitional word from the rest of the sentence.