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Could you please confirm the Intel® NUC model in question? You can check Setting Up Multiple Displays for the Intel® NUC, in this link you will find the possible configurations support for multiple for all the Intel® NUC models.
You have a NUC6CAYS or NUC6CAYH. It is outfitted with both HDMI and VGA ports. You can connect a separate monitor to each of these ports for a total of two monitors.