I have a new 24” iMac and am transferring information from a 2013 iMac. Got a thunderbolt cable to speed the process, but it only fits the old iMac as the new one has thunderbolt 4. What cable or adapter do i need to connect the two?

You need this adapter: Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple Store.

Cheers,

Jack

I'd strongly recommend you use the following procedure, while the process of connecting the two computers may work, the process below WILL work.

When you buy a new Mac the easiest, quickest and most reliable method is to simply connect the old Mac's Time Machine External Hard Disk to the new Mac using a USB cable before you turn on the new Mac. You will likely need a USB A to USB C adapter, you can find them on Amazon for $10 or less. When you start the new Mac for the first time it will startup Setup Assistant (SA), SA will get to a point where it asks if you are migrating from another computer, select Yes  and follow the on-screen prompts and it's done! It is THAT simple.

If you have already done SA on the new computer then simply connect the Time Machine External Hard Disk using a USB cable and launch Migration Assistant (MA) which is located in Applications - Utilities - MA. Then follow the on-screen prompts.

The ONLY difference between MA and SA is MA will create a new user account that you need to log into.

Both SA and MA migrate applications (not 32 bit apps) , data files, settings, it does not migrate Mac OS itself. Some professional apps such as Adobe and Microsoft apps may require re-installing their apps as they will not allow them to be migrated. As long as you kept the security keys for installing their apps, it is not a big deal.

Finally, NEVER EVER use WiFi to migrate, this will fail in almost 100% of the situations in my experience. WiFi was never intended to move large amounts of data at one time.

I use Target Disk Mode often when transferring data. It's much faster than anything else providing you know precisely what you're trying to copy.

Your transfer speed using this method depends on the available bandwidth on your old machine. Mechanical hard drives will take much longer to transfer data (300MB/s on a good day), and a SATA SSD in your Mac might do 500MB/s on a good day.

The Thunderbolt connection is 2.5GB/s which is quite fast. Your new iMac will certainly receive that much data, but your old Mac will be the one taking its time.