Version? If CC then click on Help, and Sign out on the old one. Then reinstall on the new computer. If CS6 or older, then Help > Deactivate.
Is it just Photoshop?
It appears to be CS4. I am running OS X. The computer has the suite. I transfered it via wire from one machine to the other. It will not start on the new machine. Looks like it is blocked by Adobe.
I transfered it via wire from one machine to the other.
Won't work via transfer.
You need to do a fresh installation on the new Mac.
If I bought the machine, and I don't have any discs, how do I do that?
You'll need your CS4 serial number.
Download the trial version from http://prodesigntools.com/download-adobe-cs4-and-cs3-free-trials-here.html
Follow the Very Important Instructions on that page first BEFORE you click the download links.
Install the trial then enter your serial number to license it.
Where do I find the serial number on the old Mac?
Are you saying you bought a computer with CS4 suite already installed on the computer?
There are several versions of Creative Suite 4 that have different applications depending on the version you bought.
Computers don't normally come with preinstalled software that ranges in price from approximately $600 to over $2000.
You should have the disks for CS4 somewhere or if you downloaded it, you can download again for the link in message 5 above.
And No, you cannot find the complete serial # on your old Mac.
Adobe abbreviates the serial number shown in the application.