Answer:
The sentence that is punctuated correctly is C. I live my life by this motto: "Live life to the fullest."
Step-by-step explanation:
Quotes can be introduced by a comma, a colon or nothing. Whenever the introduction is not an independent clause, a comma is usually used. Whenever the introduction is an independent clause, the quotation should be introduced by a colon. This is the case of sentence C, where the quotation is not dependent from the previous sentence as it is a complete sentence. Therefore, sentence C is punctuated correctly.