@Anja1072 There are a few things to weigh up here.
Firstly, do your house rules specify that there is an additional charge per guest after 6, or whether you allow day visitors ? Many folks don't read all the information, so it often helps to let people know things like that via messaging before they arrive e.g. in a welcome message. If you have instant book turned off, you can say something like "reservation is approved for x guests. Additional guests may be added for $y per person, to a maximum of z guests. Day visitors are included in the guest count". Using some cheerful language.
Day visitors are going to use your amenities, so it's up to you if you want to allow that or not, or state that day visitors will be charged as overnighters.
Once they are already checked in, if you are a new host, you might want to consider that you are trying to build your ratings and feedback, and sometimes it pays to let things go, at first, and chalk it up to experience.
Technically speaking, you are within your rights to request the extra funds from the guest, using the resolution center. I've done that before, and, for most people, they've been fine with settling up the difference and apologizing for their mistake. That isn't always going to happen, though. I've had people ignore me completely, and then you have to decide if it's worth chasing the extra, or not. Very often, these folks will leave no review or a not-great review.
You also have to decide how to review these guests to let other hosts know they brought additional guests.