For a rule affecting external matters outside the department's internal affairs, what is required?

The requirement for a rule that affects external matters outside the department's internal affairs is that it needs to be amended in accordance with chapter 52, title 67, Idaho Code. This chapter governs the administrative rulemaking process within the state of Idaho. It outlines the procedures for the adoption, amendment, and repeal of administrative rules, ensuring that they follow due process and are made transparently, allowing for public involvement and input.

By adhering to this process, the rules become officially recognized and enforceable, as they have gone through the necessary legal and procedural steps required by Idaho's administrative law framework. This ensures that the department's regulations align with the state's legislative intent and are subject to oversight.

The other options propose different processes that may not be applicable to the situation at hand. Public votes or endorsements from the governor, while they have their contexts in governance, do not directly pertain to the rulemaking process specified for external matters under the administrative code. Approval from the state legislature typically relates to laws rather than administrative rules, which are managed by agencies under the guidelines set forth in chapter 52.