Help needed Wix Bookings

Hi @lidia , yes, it works for sure.
Please start with Introduction - Velo API Reference - Wix.com.
You can also refer to the example:

let serviceId = // get service ID

let today = new Date();
let startRange = new Date();
let endRange = new Date();
startRange.setDate(today.getDate() + 7);  // one week from now
endRange.setDate(today.getDate() + 14);   // two weeks from now

let options = {
  startDateTime: startRange,
  endDateTime: endRange
};

return wixBookings.getServiceAvailability(serviceId, options)
  .then( (availability) => {
    let slots = availability.slots;
    let firstSlot = slots[0];
    return availability.slots
  } );

You need to run this method of every cabin service and then build a histogram of slots and get those which have the same time available for both services.