No you cannot. Intern there is only one 12V source.
If you try to put in series 2 of the +12V outputs you created a short circuit ( +12V to ground).
? WARNING ?
As you can see in the comments below @Passerby: sees some dangers in the rest of the answer which I cannot confirm yet.
But inside the power supply there is also a -12V. You can use +12V and -12V to get 24V.
This manual 'Convert a Computer ATX Power-Supply to a Lab Power Supply may be useful for you. Warning: the colors of the cables differe in a lot of ATX Power-Supplies. Always have a look at the connectors to detect which wire is the wanted.
Note from the linked web site:
The voltages that can be output by this unit are:
- 24V (+12V, -12V)
- 17V (+5V, -12V)
- 12V (+12V, GND)
- 10V (+5V, -5V)
- 7V (+12V, +5V)
- 5V (+5V, GND)
- 3.3V (+3.3V, GND)
P.s. Not every ATX Power Supply seams to have the +3.3V and the -5V