@Brian1086 If you use Instant Book, an Instant Booking takes precedence. You'd have to cancel the IB and you don't want to do that- cancellations by hosts are treated quite punitively by Airbnb.
If it's a Booking Request, the first guest you are messaging with should take precedence over another Request that comes in after- it's up to you which one you want to accept, but you would need to make a decision quickly, because you only have 24 hours to either Accept or Decline.
If it's Inquiries, I wouldn't hold the dates for that, as most Inquiries don't result in bookings, but if it sounds like a guest you'd want to host and you have a sense that they are serious about booking, then pre-approve their inquiry and let them know that they need to book ASAP, or you'll have to accept the other potential booking.
Basically, it's first to pay gets the booking.