I have recently received my first Arduino starter kit. I was able to control sequentially turning on and off 12 LEDs. I have a requirement to expand that capability to 24 LEDs. The question is can I expand the existing board or do I have to add a second independent board?
That may depend on what is supplied in your arduino kit and the code being used to operate the hardware.
Just use some shift registers. 50 cents, 8 outputs each.
74HC595 for low current (8-10mA each LED) or TPIC6C595 for 100mA each.