how to download catalina on an unsupported macbook for my older macbook

It will require booting from a Bootable Installer. 

The Bootable Installer can Only be performed on an Apple Computer 

This will have to be performed from a Qualifying Computer to run the version of macOS to be made on the Bootable Installer.

Example : Bootable Installer of Catalina would have to be done on a computer that Qualifies to run Catalina .

Notation: If the computer being used to perform this action is Too New or Too Old to qualify to run the version of macOS - this computer can’t be used.

Alternative is, to gain access to a Qualifying Apple Computer from a family member, friend or associate.

Asking for help in using or the usage of some Hacked Version of macOS.

No reputable user would assist in this matter

To expand upon @PRP_53's reply......even if you had a copy of the Catalina installer, you would not be able to create a bootable USB installer on a Mac that doesn't support Catalina. It is definitely very frustrating, but Apple only really cares about supporting the most recent version of macOS...everything else are token gestures.

Have you tried booting into Internet Recovery Mode using Command + Option + R to attempt to access the most recent version of the online installer that is compatible with that older Mac? Unfortunately some Macs may only boot to the online installer for the older version of macOS which originally shipped on the Mac from the factory. This would be Ok as well if it works (some older online installers don't always work correct.....token gestures after all) because you could then upgrade to a later version of macOS (may require several more steps & upgrades).

It would really help to know the exact model of this "broken" Mac so that we can figure out exactly which versions of macOS are compatible with it. That would allow us to tell you generally which Macs could be used to create a bootable macOS USB installer and which versions of macOS they could download & create.

You can get the exact model by entering the system serial number on the check coverage page here (please don't post the serial number on this forum since it is considered personal information):

Check Your Service and Support Coverage - Apple Support

For example, to create a bootable macOS 10.15 Catalina USB installer you generally need a Mac model 2012 to mid-2020. You can confirm a particular Mac is compatible with a specific OS by using the information in the following article since the model years I mentioned are just close generalizations and there may be some exceptions:

https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

For

• macOS 10.13 -- a model Late-2009 to mid-2018
• macOS 10.11 -- a model 2007 to 2015

As you can see there may be quite a few options for you. If you don't have access to another Mac that is compatible with an OS that the "broken" Mac supports, then you can check with other family members, friends, co-workers, or perhaps your school/employer's IT department. Or you can check with a local Apple Authorized Service Provider to see if they could assist you with accessing Internet Recovery Mode or in creating a bootable macOS USB installer.