Hmm... yeah Forge's file naming has gotten awkward for me when finding it especially around the 1.7.10 to 1.10.2 period it got awkward with 1.10.2 in different places I think, or sometimes with so many versions of Forge I have to delete them or look between the numbers properly to find it.
Anyways though, to the main topic below.
I'll have two images of the Forge versions expectations you'd be looking for pushed right down at the bottom of the versions selection list, around release 1.0.
Not the 'release 1.12.2', that's the main game/vanilla version of 1.12.2. Forge versions commonly appear below release version 1.0 of Vanilla for whatever reason, unlike say Rift or Fabric for 1.13 or 1.14 snapshots that fit more with 1.13/1.14 release versions and are called 1.13 so on Rift or 18w50a Fabric or something, but I'm getting side-tracked besides pointing it out.
And they get cluttered with numbering/versions of 1.10.2, 1.11.2 and so on so it can be awkward to find them if you still keep those versions of Forge around and haven't deleted them, or the extra versions you don't need anymore because you'd have updated to a later Forge of the Minecraft version.
Forge won't always just create the profile for you, it will create a Forge version or Forge.jar with the complex numbers in the name like you said with t he 1.10.2-forge1.10.2-12.18..3.2185, you just have to create a new profile and select the 1.12.2 Forge version below release 1.0 where all Forge versions get collated. That's all your missing. Forge only creates the profile for I think the first Forge setup, that being the 1.10.2 Forge you installed. At least I think its only the first Forge setup, I'm pretty sure it doesn't do it after that for each other version of the game you install Forge for.
I hope that helps.
If the mods don't work after sorting out the Forge situation, let me know with what mods you have by listing them to see what conflicts they could have, or posting a crash report that appears in the 'crash reports' folder of your .minecraft.
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