Q: can I switch from 32 Bit to 64 bit    The type Of My Mac Ismac os x 10.6 snow leopard and intel core duo

Snow Leopard will run both 32 and 64 bit apps. The entire OS is 64 bit. The kernel is the only exception. Depending on the model Mac being used, it may only be able to start up to the 32 bit kernel. But even so, it will still run 64 bit apps.

If your system is actually Core Duo (so, a 2006 or early 2007 Mac) then you cannot run 64 bit as the processor is not 64-bit.  You won't be able to run 64-bit apps either.  Nothing you can do but buy a new machine: Core 2 Duo was the first 64-bit Intel processor used in Macs I believe.

William is correct. Missed that it was a Core Duo. The Mac you have can't run Mountain Lion (the forum you posted in), much less 64 bit apps.

Do this to check and see what your Mac is running the system as:

Hold down the Option key and click the Apple logo at the upper left, then choose System Profiler. Expand the Software heading if necessary, then click on the Applications and the Frameworks subheadings (one at a time). The Mac will search for all installed software. At the far right will be a column for 64-Bit (Intel). Is anything marked "Yes"?

Okay, please post this info next. Hold down the Option key and click on the Apple logo at the upper left. Choose System Profiler. The very first screen that comes up is Hardware Overview. What is the model identifier, and how much RAM (memory) is installed?

That Mac's maximum OS is 10.6.8, which is where you currently are. In order to move to Mountain Lion, you'll have to purchase a new Mac.

Apple's drivers support Windows XP and Windows 7 32 bit on that Mac.