What I think you should do:
Get a switched power strip with a lamp so you KNOW when the power is OFF.
Get a 6 Volt AC supply: wall-wart, filament transformer with proper line-plug wiring, etc.
If you apply less than 1/10th rated voltage to a transformer, it won't burn-up for many minutes or hours.
Get clip-leads for your voltmeter. Don't have your fingers anywhere near any leads.
Meter one of the secondaries.
Apply the 6VAC to the (120V or) 230V primary.
You expect a "230V:24V" transformer, fed with 6V, to make about 0.6V on the "24V" secondary.
BUT if the label is wrong, and you put 6VA into a 24V winding, the winding you are measuring will be about 60V, which is somewhat dangerous. (Why you keep your fingers AWAY.)
If all is right and one "24V" winding gives 0.6V, power OFF, clip the other 24 winding, and check it.
Now clip one end of one winding to one end of the other winding, meter the end leads.
If you get 0.0V, you are correctly phased for parallel connection. Connect the end leads together, done.
If you get 1.2V, you are phased for "48V" *series* operation. That is not what you asked for; however someone else may want series.
> my oszilloskop is broken
A 'scope is a very poor tool for checking phase on two separate windings. A single-channel 'scope is always "in-phase" (the display locks to the wave). A dual-channel 'scope works IF both channels can be swept with the same sweep. However mistakes happen. The voltmeter is clear: if two leads have 0.0V between them, they are in phase; if double-voltage, they are out-phase.
Actually with the 6 Volt "dummy wall voltage", once you are SURE you didn't get pri/sec wrong, you can sorta just try all combinations with your fingers live. If wired out-phase, when you brush the wires together, they spark. In-phase, no spark, you get the expected voltage, and the transformer shows NO heat after 1, 10 or 60 minutes.