I'm using a server with two 6-core CPUs, which have 12 cores in total. Does Linux kernel supplies all these cores? How many processor cores does it support at the most? My kernel version is 2.6.34.7-56.fc13.x86_64
Linux kernel will support all the 12 cores of your CPU. It supports more than 250 CPU's, you can find the exact number of CPUs supported under your info file /usr/src/linux/Documentation. This file is present in your system.