Hi @AB21,
So I don't exactly know what your full flow looks like or where you are referencing your data values, but I created a simple set up based on some assumptions I made from your initial post.

Here's a screenshot of the flow. Basically it's an 'Apply to each' for SharePoint People values within an 'Apply to each' for particular date values (DateArray). This means that for every date, it checks every person's booking date to see if it matches.
With this condition, I increment an integer variable by 1 if the dates match. By doing so, you can check if that number is over 3, meaning that 3 or more people booked that same day.
Now for this flow, I'm not sure where you are referencing these "particular date / times," but just replace my DateArray variable with that content and it should work fine.
Hope this helps!