I have 4 sub panels in my home and I want to move two 20amp breakers from one into another. I want to run #12 Romex from the one panel too the other and use the original panel and just splice each circuit. My question if the neutral stays in the original box can I just move the hot leg
You MUST move both the hot and neutral together!
The underlying principle is currents must be equal in each cable or conduit. You can't have a situation where current flows on the hot wire from panel 4 to panel 2, but neutral just ends at panel 2 and takes a different route back to the panel (creating an imbalance in that cable too).
If currents are equal, each wire kicks a large electro-magnetic field (EMF), but the various wires are equal and opposite, so the magnetic fields cancel each other out.
Since currents are not equal, large electro-magnetic fields are kicked up. This will cause eddy current heating, and vibration -> fatigue failure on wires.
Further, neutrals do not have circuit breakers. This is safe, because neutral only handles current for its partner hot wire(s), so they handle the same current and the "hot" breaker protects the neutral. If you return current from a different path, you break that protection, and now the oversubscribed neutral can overload - and no breaker will care.