So, you are trying to summon a Fire Nymph...
PLEASE NOTE: I have created this using my understanding of how Summoning works, but I have not taken into account 'opposite' elements, because I don't know those rules. So when I say that you can breed x + y to get a Fire Nymph, and it doesn't work, please let me know in a comment, and I will edit this accordingly. And yes, I do realise I've used baby pics, but the wikia doesn't have all the teen pics yet.
Following the steps in this blog post, we know that to summon a Fire Nymph, we need both Garden and Volcano elements in the element pool...
Seeing as Garden and Volcano cannot be bred together, you need to introduce a 3rd element in the pool...
The examples I have given below are probably the easiest way to introduce a 3rd element to the element pool.
You can introduce Forest to the element pool by breeding
a Garden/Forest creature (Treant or Wisp) to breed with a Phoenix, a Volcano/Forest creature (Kapre or Kitsune) to breed with a Garden Nymph, or a Garden/Forest creature to breed with a Volcano/Forest creature:
You can introduce Sky to the element pool by either introducing a Garden/Sky creature (Fiary or Sylph) or a to breed with a Phoenix Volcano/Sky creature (Cockatrice or Wyrm) to breed with a Garden Nymph:
You can introduce Desert to the element pool by either introducing a Garden/Desert creature (Cactus Dryad or Bast) to breed with a Phoenix or a Volcano/Desert creature (Genie or Naga) to breed with a Garden Nymph:
You can introduce Beach to the element pool by either introducing a Garden/Beach creature (Nereid or Triton) to breed with a Phoenix or a Volcano/Beach creature (Water Leaper or Rakshasa) to breed with a Garden Nymph:
Obviously, you can breed 2 Hybrids with no common elements together, but then you increase the number of other outcomes from 5 to 11, so why bother???