Can I use my license on another computer in my possession? Method

Yes.

From the Vegas Pro Support Help Centre:

To unlock the MAGIX software on another computer, use the serial number provided. If you exceed the maximum number of devices that can be used simultaneously, as specified in the serial number, you must deactivate a device that has already been activated in order to use the product on another computer. You can do this either directly in the program or in the MAGIX Service Center. In the MAGIX Service Center you can find your activated serial numbers and activations under "My products".

If you installed Vegas Pro on your first computer using either the installer or the .exe. file/s, just do the same on the other computer.