It will depend on the version of iPhoto that you are currently using on your Mac with OS X 10.6.8 Snow Leopard. If the version number of iPhoto is starting with 9 (for iPhoto '11) or 8 (for iPhoto '09) you can simply copy the complete iPhoto Library to your new Mac into the Pictures folder, or transfer it on an external drive to your other Mac; the drive needs to be prepared as described here for Photos: Move your Photos library to save space on your Mac - Apple Support
Once the iPhoto Library is on your newer Mac, ctrl-click it, then select "Open with ..." and select Photos. Photos will create a Photos Library from your iPhoto Library.
If the iPhoto version on your old Mac is older than iPhoto '09 (version numbers starting with 7 or less), the iPhoto Library needs preparing with the iPhoto Library upgrader (see: iPhoto '11: About the Library Upgrader), otherwise the Photos.app will not be able to create a Photos Library from it.
You have to run the iPhoto Library upgrader tool on your old Mac, because it contains 32-bit code and can only run on a Mac with macOS 10.14 or older.