My Iphoto don't work after update

iPhoto was discontinued 6 years ago. Photos is the new Photo management software.

To use Photos, Launch it with the option key held down. From the resulting dialog, choose your iPhoto Library. Photos will create a new library from your iPhoto media.

iPhoto was discontinued 6 years ago. It is no longer developed or sold. It was replaced by the more powerful (and free) Photos.app that comes with the OS. You can migrate to that app very simply:

Hold down the option (or alt) key and launch Photos. From the resulting menu select 'Choose Library' and point at your iPhoto Library. It will do the rest.

If you prefer not to use Photos there are several 3rd party apps that you can use. Which to choose depends on the kind of photographer you are and your budget.

macOS 15 Catalina is the first system version, that is only supporting 64-bit code. All older system frameworks, that have been 32-bit are no longer installed by macOS 15 Catalina and all recent system version. iPhoto needs old iLife framework, that are no longer available, so it can no longer run on Catalina, even if it is a 64-bit application. The transition to 64-bit only has been the final straw breaking iPhoto completely, after Apple stopped the development of iPhoto in 2015.