How do I increase axle speed using gears How do I increase speed of my output axle 24 times using 8, 16, 32, and 64 tooth gears using LEGO Mindstorms components? I checked Sariel's website but it was no help.
You can't do this with the gears you've listed, but I'm not sure that you've listed the proper gears. I don’t believe that 32 or 64 tooth gears exist. I at least don't have any.

You can do this by combining common 8, 16, and 24 tooth gears. The following gives 3:1 × 2:1 × 2:1 × 2:1 = 24:1.