Eggy Hatchy kind of works similar to a breeding simulator.
A Moss Egg merged with a Fire Egg could give: Moss, Tree, Forest, Snootroot, Fire, Flower, Poison, Pepper, Smoulderbrush, Lava, Obsidian, Burrow, Soot
Add four or more elements and you can have Rainbow, Double Rainbow, Triple Rainbow (and this event Quadruple Leap Year since it is currently available to breed)
Similarly, some epic dragons may have latent breeding elements that aren't seen that could result in a possibly unexpected hybrid or epic dragon.
The circle with the number in it tells you the least amount of merges needed of what it is asking for. For example, if it has Fire element with the number 3, then that means at least three merges need to happen to get an egg with a Fire element to bank.
Sometimes you need to do this multiple times and it will tell you how many times it wants a Fire element with at least 3 merges.
An additional note with merges is that if the two eggs are the same the merge number will increase by 1, a Lava egg with 1 and a Lava egg with 1 will give a Lava egg with 3.
Other than the merge requirement and the element, a second type of request is total points banked.
Twin eggs will double the value of what the egg would be as a standard egg. Epic eggs will bank more points than common hybrids. Some eggs are presented as twins and sometimes you may be able to make an egg a twin if you cross your merge over one of those blue and white eggs in the background.
Part of Eggy Hatchy is also luck. You can be very strategic and combine the right elements, but the simulator may give a Tree egg when merging Moss and Firefly rather than Rainbow which would give more points. It may give you Obsidian instead of something with earth element to fulfill an earth element requirement.
I know I've had to try some levels multiple times just because of a lack of luck.
Hopefully some of this helps.
There are also screen captures of a tutorial of Eggy Hatchy on the Eggy Hatchy wiki page:
https://dragonvale.fandom.com/wiki/Eggy_Hatchy
The wiki also has a breeding sandbox simulator to test out what may come out. Currently the wiki is updating the availability of all the dragons in the event market so some of those may not appear at the time of this post.
https://dragonvale.fandom.com/wiki/Breeding_Rules
