How can I hide the fax numbers from the address book?

If you don't use the fax numbers to send faxes from the computer, the easiest way would be to write some signs in front of the number (e.g. "Fax ").

Therefor choose the action Add in front of and in the field selection All Fax Numbers.

But if you use the numbers to send faxes from your computer, it's recommended to move the numbers in another telephone number field (e.g. Other, Pager etc.).

The same is the case for addresses from the Business Contact Manager, because the prefix of letters in front of numbers has no consequence for the view in the address book.