Hi,
The plugin you are using is a different one, the “Appointment Hour Booking”, however the answer to this questions is similar: there is some plugin or server setting removing the session cookies, causing that the captcha cannot be verified. Please check if you have some plugin that may be removing cookies and check if your server is allowing sessions/cookies for the public website (a CDN may be also the one removing the cookies).
In the meantime disable the captcha until finding the cause and solution for the cookies issue.
Thank you for using our plugins!