I am not an electrician but i do plenty of electrical work. I believe what you a looking to do is create a "multiwire circuit". You can Google that for more information.
At the house end get a double pole 20 amp breaker and hook the red wire to one pole and the black wire to the other pole and install that breaker in the main panel. At the garage end use the black and white for one of your circuits and the red and white for the other circuit.
As i understand it, the shared neutral on this configuration is perfectly legal as long as one handle on the breaker shuts off both circuits. Using a double pole breaker puts each circuit on a different phase so that the neutral will only carry the difference between the two circuits rather than the additive if the two circuits were on the same phase.
I am sure others here can explain it more clearly than i have done. Good luck!
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