I would like to run a new circuit to my garage logically wired as below.
This would give me two 120v 20 amp circuits that I need and would give me a 240v 20 amp circuit as well.
I would use a double pole breaker so if either side goes they both go.
Is there anything wrong with this?
1. If you wan to make it permanent, it would be better to use a double-throw security switch, so there would be no overloading possibility,
as I imagine that your circuit breaker must 20 A, and isolate the 120 V from the 240 V.
I would also recommend using GFCI (Ground Fault Circuit Interrupter) 20 A plugs and circuit breaker.
2. If you wan to make it temporary, for example you want to be able to plug a 12 V battery charger, or a vacuum cleaner...
You could build a DIY extension for that special occasion.
I had some extra wires, so I build this extension that could be useful to have, while I would be careful for not overloading the circuit.
I use a NEMA 14-50 input plug to convert to a NEMA 10-30 receptacle because the TESLA Gen2 portable UMC 14-50 adapter was sold out.
By the same occasion I added two single phase NEMA 5-20 GFCI plugs, as this can be useful.
Also, this was a way to test that the original NEMA 14-50 wall receptacle was correctly wired and grounded,
using a simple single phase GFCI tester.
Here is below the NEMA 14-30 to 10-30 and 5-20 GFCI extension.
I used AWG 10/4 SO for the cord and AWG 14 to wire the 5-20 plugs.