What action is the governor prohibited from taking regarding referendum or initiative measures passed by the people?

The governor is prohibited from vetoing referendum or initiative measures that have been passed by the people. This principle is rooted in the idea that these measures represent the direct will of the electorate. The purpose of referendums and initiatives is to give citizens a direct voice in legislation, allowing them to bypass the traditional legislative process when they seek to enact or change laws.

When the people vote on such measures, it reflects a democratic decision that cannot be undermined by the executive branch, which includes the governor's veto power. In this context, the governor is not allowed to interfere with the outcome of these votes through a veto, thus ensuring that the voice of the constituents remains paramount in matters of law that they have specifically chosen to address.

While the other options—approving, delaying, and amending—may involve levels of interaction with the legislative process or administrative action, they do not fundamentally challenge the prerogative of the electorate to enact laws through referendum or initiative. The key aspect is that once passed by the voters, these measures become law without the governor's power to issue a veto.