How do I transfer data from my old MacBook Air macOS Mojave 10.14.6 to new MacBook Air?

If the old Mac has Thunderbolt 2 ports with old-style Mini DisplayPort connectors, a Thunderbolt connection is not the best way to solve this problem. You'd to spend $50 on an Apple Thunderbolt 3-to-2 adapter, and another $30+ on a hard-to-find Thunderbolt 1/2 cable – hardware that you would likely use only once.

Migration Assistant can work from an external drive containing a backup of your old Mac. That drive can contain a Time Machine backup, or a bootable clone backup made with Carbon Copy Cloner or SuperDuper!, whichever you happen to have on hand. Then you don't need a direct connection between the two Macs.

You might need to overcome the USB-A vs. USB-C difference, but there are a number of ways of doing that, one being the Apple USB-C to USB adapter.

What model year of MacBook Air is the one running Mojave? Or at least what ports does it have?

In general you will want cables that can connect to both Macs.

For a current MacBook Air that would be a USB-C / Thunderbolt 3,4,5 cable to whatever the old one has. Likely a thunderbolt 2 port, which may require an adapter.

For example: Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple.com. and then a thunderbolt 2 cable to connect the adapter to the old Mac.