Java 32 and 64 bit???

I'm about to start working a job that is done online. The company's software is now available for use on MAC's!!!

Anyways, in order to use their software, I need to "re-arrange" my Java Preferences.

Their directions tell me to go into Java Preferences and drag the "64-bit" option to the top.

The problem is...... I do not have a "64-bit" option!!! I just have one option in my menu and it's "32-bit".

Here is that option exactly:

Java SE 6 Apple Inc. 32-bit 1.6.0_43

The company I am working for is telling me that my computer might be too old to support their software.

Do you think they are correct???

Is there any way to get my Java upgraded to 64-bit???

I do have an old Macbook Pro from 2006.....the original.

Thank you for taking the time to read this. Please let me know if you have any ideas.

-Dick Zulu