The question asks to complete the sentence: "Local government is authorized to pass ....." A by-law (often spelled bye-law) is a rule or law made by a local authority or corporation. Local governments have the power to enact multiple such rules to govern their jurisdiction. Therefore, the plural form is generally used when referring to this power. Let's examine the options: A. Bye-law - This is the singular form. While a local government can pass a single bye-law, the general authorization implies the ability to pass multiple. B. Bye-laws - This is the correct plural form of "bye-law". This accurately reflects the authority of local governments to enact various regulations. C. Byes'-laws - This uses an incorrect possessive apostrophe and pluralization. D. Bye's-law - This uses an incorrect possessive apostrophe. The most appropriate option to complete the sentence, indicating the general power of local government, is the plural form "Bye-laws". The final answer is $\boxed{\text{B}}$